Birkbeck and Kings are both part of the University of London. The U. of London is an umbrella organisation that incorporates a group London unis including LSE and UCL. Birkbeck is geared towards mature students, and offers lots of part-time, and evening courses.
University of Westminster is a newer university and former polytechnic, so will offer more vocational courses. There is a separate business school within the uni.
As others have suggested, I would definitely check the league tables.