Agree with James that Westminster's location is good. Meanwhile, so is Birkbeck. Both are close to the political heart of London. In this perspective, I believe Birkbeck is slightly better; it's in Russell Square in Bloomsbury, circled by UoL Senate House and other UoL brother colleges, including LSE, SOAS and UCL, and King's is just a while's walk. Birkbeck fellows are welcome to use the resources there, engage with that community and easier to join their activities, which are somehow significant to ones who are studying politics.
Upstairs '4750946' is spreading nonsense things about Birkbeck's rankings, and good to see Bloomer and Axis are providing correct clarification. For example, according to THE2022 'Politics & International Studies', Birkbeck is ranked 30+, while Westminster is 80+; in terms of 'research' and 'citation', Birkbeck's scores are double of Westminster in both indicators.