Member of Parliament, often shortened to MP, is the correct title for a member of the British Parliament!
Technically, anybody who is a member of the House of Commons or of the House of Lords can use the title, but traditionally, it is only used by members of The Commons. When Parliament is dissolved in preparation for a General Election (as is likely to be announced today), all the MPs are no longer MPs, and no longer have the right to use the letters after their name, until they have been re-elected. Some MPs have run into problems with their websites in the past - they have used, for example, (and I don't know if Mr Blair did this), "www.tonyblairmp.com". However, they have been told they can't use this while they're not actually MPs!
The Houses of Parliament are within the Palace of Westminster. Although this is within Greater London, it isn't in the City of London and is actually in the City of Westminster. As well as the chambers and other services, most MPs have offices either in the Palace, or in Portcullis House, a brand new office block across the road.
Members are afforded various privileges - for example, they can't be taken to court for anything they say while in the house. There are also bars that are allowed to open longer than the usual hours, and various other advantages.
mr100percent says MP is also used for other Parlimentary governments as well, India, Pakistan, etc. and of course he's correct, it is used in a number of other countries. I wonder if it's related to the British Empire?