What museums and galleries were open to Londoners in 1938? I have a pre-war A-Z with a gazetteer of Places of Interest so I can look them up. Here's a list of all the places they listed with an admission price, free or otherwise. The most intriguing sub-list is the last one.
(For the benefit of readers younger than me, 6d = 2½p, 1/- = 5p, 1/3 = 6p, 1/6 = 7½p)
Was free, still free
» Bethnal Green Museum (now the V&A Museum of Childhood)
» British Museum
» Chelsea Royal Hospital
» Geffrye Museum (now the Museum of the Home)
» Guildhall & Art Gallery
» Horniman Museum
» Imperial War Museum
» Ken Wood
» Museum of Practical Geology (now part of the Natural History Museum)
» Natural History Museum
» Royal College of Surgeons (now the Hunterian Museum)
» Royal Exchange (now shops and services)
» St Bartholomew's Hospital Museum
» Science Museum
» Soane's Museum (now Sir John Soane's Museum)
» Southwark Cathedral
» Temple Church
» Victoria & Albert Museum
» Westminster Cathedral (but lift 1/-)
» Westminster Hall
Now cheaper on Fridays than they were in 1938
» National Gallery (free except Thu, Fri 6d)
» National Portrait Gallery (free except Thu, Fri 6d)
» National Maritime Museum (free except Fri 6d)
» Wallace Collection (free except Tue, Fri 6d)
Now cheaper midweek than it was in 1938
» Tate Gallery, Millbank (free except Tue, Wed 6d)
Special access arrangements
» Buckingham Palace (permission to visit the Royal Stables can be obtained by writing to the Master of the Horse)
» Goldsmith's Hall (admission usually obtainable on written application)
» Royal Mint (written application to be made in advance to the Deputy Master, parties not to exceed six)
No longer free
» Dulwich Picture Gallery (now £16.50)
» Leighton House (now £9)
Partially free in 1938
» Royal Academy of Arts (permanent galleries free, annual exhibition 1/6) (exhibitions now £17-£22)
» St Paul's Cathedral (free, Crypt 6d, Whispering Gallery & Stone Gallery 6d, Golden Gallery 1/-, Ball 1/-) (now £17)
» Westminster Abbey (free, but ambulatory & chapels 6d) (now £18)
Admission fee has increased somewhat since 1938
» Charterhouse (was 1/-) (now £15)
» Dickens's House, 48 Doughty Street (was 6d) (now £9.50)
» Hampton Court (was 1/- weekdays, 6d Sat, free Sun) (now £25.30)
» Kew Gardens (1d, Tue and Fri 6d, bank holidays free) (now £17.50)
» Madame Tussaud's (was 1/3, Chamber of Horrors 6d extra) (now £30.50)
» The Monument (was 3d) (now £5.40)
» Tower of London (was 6d, Jewel Tower 6d, Bloody Tower 6d) (now £28.90)
» Zoological Garden (1/-, except Mon 6d) (now £29.50)
No longer open
» Cuming Museum, Walworth Road: Its relics of the Stone age and the civilisations of Babylon, Egypt, Greece, Rome and Mexico illustrate the development of man's work from prehistoric to recent times. (free)
» Duke of York's Column, Waterloo Place: View from top. (6d)
» Royal United Service Museum, Whitehall: Occupies Inigo Jones's Banqueting Hall. The museum deals with the naval and military history of Great Britain and contains a collection of arms, armour, models and relics. (1/-, soldiers & sailors free)
» Home Office Industrial Museum, Horseferry Road: Contains exhibits of methods and appliances for the promotion of safety and health amongst industrial workers. (free)
» Imperial Institute, Imperial Institute Road: In order to promote an interest in the Empire, the exhibits show the geography, resources and commercial products of each country. (free)
» India Museum, Imperial Institute Road: A branch of the Victoria & Albert Museum devoted to the portrayal of the life, art and religion of India and its surrounding countries. (free)
» London Museum, Lancaster House: Illustrates the domestic and social history of London from pre-Roman times to the present day, and includes a collection of costumes associated with the Royal Family. (free, but Tue 1/-, Wed & Thu 6d)
» Parkes Museum, 90 Buckingham Palace Road: Contains exhibits relating to modern hygiene in architectural and food values, disinfection etc for the prevention of disease. (free)
» Public Record Office, Chancery Lane: Here amongst other interesting documents are to be seen the Domesday book, papers concerning the Gunpowder Plot, a letter from George Washington to George III and the log book of the Victory.