The principle contemporary works on Henry VII are Polydore Vergil's Anglica Historica (1534) (which Henry himself commissioned), Sir Francis Bacon's History of the Reign of King Henry the Seventh (1621) and the writings of lawyer Edward Hall in the 1540s. Bacon's work remained by far the most comprehensive and general until S. B. Chrime's Henry VII was published in 1972.
Node your revision. I think this summarizes everything you need to know about Henry's foreign policy for AS History (UK), probably more. The chronology of events (annexation of Brittany, Simnel, Warbeck, Bosworth, etc.) tend to be noded elsewhere (and are linked to), this is an analysis of Henry's foreign policy as a whole. If an event is undescribed here and un-noded elsewhere, please /msg me and I shall rectify the error.
Introduction
If there is any area in which Henry VII can be said to have claimed success by the end of his reign, it is in his foreign policy. While a changing international scene often made Henry appear erratic in his aims, he was in fact resolute and steadfast in them. Henry's policy was above all realistic, and he did not aspire to pretension, realizing that England was not the power it once was.
The only foothold which England had on continental Europe was Calais, the rest of the spoils of the Hundred Years' War having being recaptured by the French in the fateful reign of Henry VI. Unlike his predecessor, Edward IV, Henry did not have unrealistic ambitions of re-establishing an English Empire on French soil. The newly-unified and powerful France was capable of fielding an army and flaunting a treasury much in excess of England's.
Professor Chrimes split Henry's foreign policy into three phases: 1485-92 (which was the development of English diplomacy), 1493-1502 (which was when Henry's diplomacy began to bear real fruit) and 1503-09 (when the European scene was changing rapidly). English diplomacy is best considered in relation to the main powers near them - Burgundy, France and Spain. Scotland is also worthy of consideration, as England is only half an island.
1. Over-riding issues
a) The security of Henry's dynasty
Henry was the first monarch of the House of Tudor, which would be with England for another century yet. However, he was not to know how secure his dynasty was (especially given that the Crown had changed hands so frequently and with much bloodshed during the War of the Roses). Henry's most immediate goal was always to make sure the next man to sit on the throne of England was the fruit of his loins. Hence Henry had to sire a successor and secure the international climate for his succession.
Arthur was born to Henry by Elizabeth of York in 1486, merely a year after he came to the throne. This was glorious news, and equally glorious was the agreed marriage of Arthur at age 3 to Catherine of Aragon, securing a close relationship with the Spanish. This marriage alliance legitimized Henry's dynasty as it was being recognised as an equal by an established ruler of Europe. Henry had to deal with the pretenders to his throne (Lambert Simnel and Perkin Warbeck) quickly to placate the Spanish, who did not want to be marrying into an insecure dynasty.
When Arthur died in 1502, Henry's only remaining son was Henry who, despite his future prowess, was considered weak and feeble. Upon the death of Prince Arthur, Ferdinand and Isabella of Spain worked quickly to ensure the marriage of Catherine of Aragon to Prince Henry (thus the conditions for the divorce case and the English reformation were set).
b) The pretenders and remaining Yorkists
The Yorkists were relations and supporters of Edward IV and really a relic of the War of the Roses, of which the Battle of Stoke is considered to be the last. Although there was no "Yorkist party" now and the citizenry seemed tired of civil strife1, foreign powers which held a grudge would often seek to intervene in English affairs. The Irish always supported any challenger to the English crown, especially a Yorkist - and Margaret of Burgundy was a relation of the Yorkist King Edward IV. Much of Henry's foreign policy was directed by his attempts to gather international support for his dynasty and destroy support for its enemies. The treaties of Medina del Campo with Spain (1489), Etaples with France (1492) and the Truce of Ayton with Scotland (1497), all contained clauses forbidding these countries from harbouring English rebels.
2. France
France was England's traditional enemy, but as has been noted they now vastly out-classed her in terms of military and financial might. When Henry ascended to the throne in 1485, he did so by force at the Battle of Bosworth, and as his hereditery right was weak he needed time to consolidate support at home without French interference. Thus he established a one-year truce with the French as soon as he came to power, but it was them that would provide him with his first major crisis, both internationally and (indirectly) domestically.
In the late 1480s, the French regent began to make moves which would result in her annexing Brittany. Henry greatly feared this, as it would leave all of the south side of the channel but Calais in French hands. Not only this, but he owed great debts to both the King of France and the Duke of Brittany. The King of France had financed the Battle of Bosworth, and the Duke of Brittany had harboured him and his uncle in all their years of exile from England.
After experiencing internal strife in 1487 when he taxed the people to pay for an expedition to defend Brittany, Henry decided to employ his brutal pragmatism. French attention was gradually being turned to the Italian Wars, and in a calculated move Henry landed a nuisance army on the shores of France and laid siege to Boulogne (as his son would do). Within nine days the Treaty of Etaples was signed to make Henry go away, and Henry received a generous pension and the promise that English rebels would be expelled from France. Henry had saved face and shown England was still worthy of consideration in European power games. France annexed Brittany.
3. Burgundy
During the wars with France in the last century, Burgundy had been England's staunchest ally. However, this situation could no longer continue - the Duchess, Margaret of Burgundy, was Edward IV's sister and had been providing troops to the Yorkists in the recent civil war. Although trade with Burgundy was important to England, Henry showed no hesitation in placing an embargo on Burgundian cloth to try and dissaude Margaret and Philip of Burgundy to stop supporting Perkin Warbeck.
The Magnus Intercursus was signed in 1496, but in 1506 this was replaced with the Malus Intercursus when Philip was shipwrecked in England and forced to capitulate. He was also forced to hand over the Duke of Suffolk, Edmund de la Pole, who had been taking refuge in Flanders, the traditional meeting place for Yorkist dissidents.
4. Spain
Spain was a new power in Europe, as it had recently been unified by Ferdinand of Aragon and Isabella of Castile. Henry concluded a treaty with them relatively early in his reign (1489), mostly upon the lines of mutual dislike for the French. Amiacable relations continued between the two, and Yorkist rebels never found a safe harbour in Spain.
Upon the death of Isabella of Castile, the unity of the Spains appeared to be in danger. Philip of Burgundy, married to Joanna the Mad, had the principal claim to Castile. Not only that, but Henry and Ferdinand were now rivals in the search for a wife, Elizabeth of York having died in 1503. With Spain and Burgundy now at odds, Henry's tri-partisan force against France looked in danger of breaking. As it now looked like Ferdinand of Aragon would become a third-rate power, Henry began to make overtures to Burgundy.
However, everything changed upon the sudden death of Philip of Burgundy in 1506. Joanna went mad with grief, and Ferdinand took control of Castile. Not especially pleased by his erstwhile ally's turn of fate, Ferdinand allied with France in the 1508 League of Cambrai, excluding Henry. For his part, Henry continued his overtures to the new Burgundian regent and her father, Margaret of Savoy and Holy Roman Emperor Maximilian I. The League, which had been overtly called together to crusade against the infidel Turk, did not really threaten England's vital interests. In fact, it shifted the European focus south to Italy, away from Henry in his twilight years.
5. Scotland
Scotland often provided assitance to France in their joint efforts to annoy the English, as the Scots resented their obligations to the English crown. Henry negotiated a truce for several years when he came to the throne, and in 1488 he had the further good fortune of the Scottish King, James III, being assassinated. The 15 year old James IV ascended, and extended the truce, but as a minor he was not willing to cause Henry trouble until he at least came of age.
But, predictably, when he did come of age, James IV began to offer support to Perkin Warbeck in 1495. He even offered his cousin's hand in marriage to Warbeck, and financed border raids. While these raids were massively unsuccessful, they were a nuisance to Henry and caused a rebellion in Cornwall when he levyed taxes to pay for the realm's defence. Eventually, James lost faith in Warbeck, and concluded the Truce of Ayton with Henry in 1497. This was quite an achievement, as such a treaty between the two countries had not been concluded until 1328.
Conclusion
Polydore Vergil wrote that the King was "most fortunate in war, although he was constitutionally more inclined to peace". Henry tried for peace wherever possible, and his only real action of war was the defence of Brittany and "invasion" of France, which was in fact more of a calculated move to extract money from the French King. He concluded successful treaties with Spain and Scotland, and trade pacts with Burgundy. Although towards the end of his reign changing international conditions called into question the validity of his actions, he had acted as best he could at any time.
Similarly we must not over-estimate what the King's resources allowed him to do - within the framework of having to protect his dynasty at home and a lukewarm nobility, Henry performed admirably. He ensured the succession of his son undisputed, something that had not happened in English politics for quite some time.
~ Notes ~
1. While the citizenry did not seem to want to encourage civil strife for the sake of such, as evidenced by their lack of support for dynastic challenges to Henry VII, there were tax rebellions in 1489 and 1497. These seemed to show their apathy to the defence of Henry's dynasty as well as its overthrowing!