Members of Parliament
Here's one you may not have heard of: Stephen Lloyd, the Liberal Democrat MP for Eastbourne since 2010, has claimed that he appeared in both Doctor Who and 'Allo 'Allo under a stage name during his brief acting career in the early 1980s. My intense research of IMDB suggests that he may have been Ray Float, who appears briefly as the UNIT sergeant at the start of The Five Doctors (1983). I am not totally convinced as Ray Float has much more impressive eyebrows, but who knows what happens to one's eyebrows in thirty years?
More obviously, Ann Widdecombe, the Conservative MP for Maidstone and the Weald from 1987 to 1997, appeared as herself in The Sound of Drums (2007); of the couple of dozen people who have played themselves on Doctor Who, I think she is the only politician.
Members of the House of Lords
Sal Brinton, Baroness Brinton since 2011, worked on a couple of Doctor Who stories as a production assistant in the late 1970s. I once asked her for more details, but failed to note the answer - I think Horror of Fang Rock (1977) was one of them.
Floella Benjamin, Baroness Benjamin since 2010, appeared as Professor Rivers in four out of the five series of The Sarah Jane Adventures. Like Sal Brinton she is a Liberal Democrat.
(The Earl of Portland, who was briefly a member of the House of Lords before the 1999 reforms, has appeared in two Big Finish audios; I do not know his then party affiliation if any.)
Member of the European Parliament
Michael Cashman, Labour MEP for the West Midlands since 1999, played First Officer Andrew Bilton in Time Flight (1982).
I am sure that this can be only the tip of the iceberg; David Tennant is of course a Labour Party activist and may end up playing a different role some day; Cheryl Hall, who played Shirna in Carnival of Monsters (1973), missed out on a parliamentary seat in 1997 by less than 4000 votes and was at one time leader of the Labour group on Kent County Council. I look forward to further enlightenment in comments.
Edited to add: Andrew Hickey reminds me in comments of the unsuccessful political efforts of Richard Franklin.