All scenes involving Wilfrid Hyde-White were shot in California, as he was then a British tax exile, who owed thousands of pounds to the Inland Revenue in Britain.
Only certain location shots and one interior scene (Columbo's visit to Superintendent Durk's gentleman's club) actually were filmed in Britain. The rest of the studio scenes, and all those taking place at Sir Roger's country house, were done in California.
Interior and exterior sequences filmed in California were photographed by the regular Columbo director of photography, Harry L. Wolf, but the London exterior sequences were lensed by the late, distinguished, two-time Oscar winner Geoffrey Unsworth, whose work included 2001: A Space Odyssey (1968), Superman (1978), Tess (1979), and Murder on the Orient Express (1974).
After his character collects Columbo from Heathrow Airport, John Fraser, who has spent nearly all his career in the UK, appears only in scenes filmed outdoors, as part of the restricted filming in Britain.
The exterior building used as the London Wax Museum was, in fact, the Royal College of Music.