Where can I get a breakdown of British members of parliament by party and nation (England, Scotland, Wales, N. Ire.) after each national election?
Well, not really, unless I’m missing something. I could use that page to create the kind of table I’m looking for (Party on one axis, nation on another; like this) for the current parliament. But what about previous parliaments?
And it’s slightly easier to read the information on Wikipedia
NI MPs by party
MPs for Scotland by party
I’m not having much luck with Wales and England yet
http://www.election.demon.co.uk/ and especially http://www.psr.keele.ac.uk/area/uk.htm seem to offer what you need - bear in mind that total numbers of MPs change, significantly so in the last election with completely redrawn constituencies for Scotland.
There’s good maps for the last two election here: http://news.bbc.co.uk/1/shared/vote2005/flash_map/html/map05.stm
Note that the situation in the last American election, where a fairly even vote left the map apparently drowned in red, is even more evident here. Labour’s support is dominant in the cities, and therefore many red seats are tiny constituencies in London, the north and the central Scottish belt. Many Tory seats are large rural ones, so blue dominates the map. And the huge chunk of Lib Dem orange in northern Scotland is actually only about half-a-dozen seats.
Somebody’s got an interest in UK politics 
Well, it’s about time.
Thanks for all the info, folks!