The British Isles is rich in the number and diversity of its museums and galleries. In the United Kingdom there are over 2,000 in all, fewer than 30 of which are funded by central government. Many museums hold collections of Coleoptera which may be inspected by bona fide coleopterists, including some small and private museums for which special visiting arrangements will have to be made.
To find your local museum go to Natural History Near You, which provides a map of natural history museums, maintained by the Natural Sciences Collections Association (NatSCA).
NatSCA also host the FENSCORE database, which provides details about particular collections within the museums. FENSCORE provides both a searchable national database of collection information, and to provide current and archive information about collections research in the British Isles. For example, here are results for a search on the term "Coleoptera".