It's not going to be easy.
London (or, at least, the central part of it) is largely made up of fairly distinct districts. For example, nearly all of the financial institutions are in one area, whereas the majority of major theatres are all huddled together in a different one.
So it is with Chinese restaurants/buffets. They are, perhaps unsurprisingly, largely around Chinatown, which is served by Piccadilly Circus and Leicester Square Tube stations. Neither of those stations is served directly from Westminster. (You'd need to change at Embankment unless you walked the half a mile from Westminster to Embankment to eliminate the first Tube journey). Most people would probably walk from Westminster to Chinatown but it might be a bit too far for your group. (The 24 bus runs from Westminster to Leicester Square though. It's only a coupe of stops).
If you can get to Chinatown though, MW Buffet (on Wardour Street, not far from Piccadilly Circus station) is inexpensive:
http://mwbuffet.co.uk/mw-buffet.html
Hong Kong Buffet (on Lisle Street, not far from Leicester Square station) hasn't got a price on their website but, given the amount of competition that there is in the area, they shouldn't cost an arm and a leg either.
https://www.hongkongbuffet.org.uk/