At 03:25 is a shot of Duddingston Village and Loch which are part of the Queen's Park, Edinburgh, which contains Holyrood House (the Royal Palace) and the prominent hill Arthur's Seat overlooking Edinburgh.
At 05:46 is a Cathedral, which I'm pretty sure is that of Lincoln, England. Whether the immediately subsequent footage is also Lincoln I'll try and check with someone who lived there whom I know.
At about 01:13 there is a grey car showing head-on at Edinburgh Castle, which is a 1953-55 'Opel Kapitän' made in Germany. I, by coincidence, have a Kodachrome slide of this spot, taken I presume at the same time, which shows exactly the same car. That photo was taken in August 1962, and I think the Edinburgh part of this film dates from the same month. At one point in a sequence of the two ladies on the Castle Esplanade you can see some un-erected scaffolding poles just on the left hand side, which would have been used around the time for seating on the Esplanade for the Festival Tattoo that month. An additional confirmation of the date is at 01:38, where the Royal Scottish Academy at the foot of the 'Mound' is pristine, having been cleaned from approx Aug 1961 to Aug. 1962, while its neighbour the National Gallery hasn't been, as that cleaning did not start until autumn 1963, finishing in autumn 1964.
Here's the info provided by the friend I mentioned, which answers most of the questions about the places between Edinburgh and London: 05:35 Pyewipe Inn is close to the railway a few miles west of Lincoln: goo.gl/maps/rL3PWQkB7UBfcnii7 . So the goods depot at 5:40 must have been the Holmes yard at Lincoln, apparently taken when the train was waiting to enter Lincoln Central station; the camera then pans to a view of Lincoln cathedral and the train gets moving again. 06:00 is still at Lincoln, showing Brayford Pool and wharf - www.photrek.co.uk/?page_id=998 shows the Holmes yard at Lincoln in relation to Brayford Pool (called Brayford Mere on the plan.) 06:10 houses look, in style, as though they are in Lincoln, but I'm not sure exactly where. But 06:16 is Elm Hill in Norwich: goo.gl/maps/YXjdxJ156JFAGnCfA . 06:35 is Norwich Cathedral, i.e. the Church of England one (seen from the castle, probably: www.tripadvisor.com/LocationPhotoDirectLink-g186342-d571520-i36830766-Premier_Inn_Norwich_City_Centre_Duke_Street_hotel-Norwich_Norfolk_East_Ang.html ) 06:52 Norwich City Hall with the Roman Catholic Cathedral beyond, probably also seen from the castle.