There is a surprising number of Museums and Art Galleries in Britain with copies of his work in their collections.  They include, in no particular order:

• The Ashmolean, Oxford
• The British Museum
• The Victoria and Albert Museum
• The National Portrait Gallery
• The Royal Collection, Windsor Castle
• Plus numerous regional museums and art galleries

In other countries:

• National Gallery of Victoria, Melbourne, Australia
• NGA, Canberra, Australia
• Auckland Art Gallery, New Zealand

Please note that in most cases the Henry Rayner works are not on permanent display, so if you are planning a visit you should check in advance whether it is possible to see them, and if so what the viewing arrangements are.