Yes, the Natural History Museum(BM) has a superb collection of meteorites. Many years ago I was privileged to be able to view some of the stored specimens. A rare opportunity indeed. The NHM, however, is very much a working museum for scientific analysis and so most of the meteorite collection is not on display and cannot be accessed by the general public. There is however some information about meteorites on the museum website which you may find of interest if you haven’t read this already.
British Astronomical Association
Supporting amateur astronomers since 1890