Two characters discuss the fact that they are getting rid of the trams and how when they next dock in London they will probably be gone, also Leslie Phillips gives directions by bus and tram to Camberwell Palace."
Several London Transport trams feature here, firstly E1 599 (first shot lightened slightly) - the inside footage is a studio mock up:
Night views of roofbox RT400 (HLX217) include a platform shot:
These daytime RTs are too distant to identify!
Nor can this E1 tram be picked out......
....but it's likely it's 573, seen as part of the same sequence:
Remaining views of buses and trams are too dark to screencap, but Jon Price also reports
a Bedford OB crossing Tower Bridge.