On a recent visit to the Tower of London a Yeoman Warder told us of a likely origin of this nursery rhyme explaining that such rhymes were a common way of teaching history in those times (16th Century) - reading and writing were no so common.
In it the farmer’s wife indicates Queen Mary I (thus named perhaps for her looks or for the composition of her estate) and the mice are three men she had burned at the stake for their allegiance to the Protestant faith (Mary being a Catholic).
It is quite possible they refer specifically to the Oxford Martyrs (Hugh Latimer, Nicholas Ridley and Thomas Cranmer) the most famous of the 300 she executed in her reign.