It's a brief glimpse during the initial ambulance run sequence when the camera follows an ambulance along Queen's Road Central before heading up into the hills to the hospital.
The way the film is edited we are given to believe that the ambulance is on the road to the hospital - which would mean Conduit Road - however, a closer inspection of some of the buildings in the background have revealed that we are actually seeing Peak Road on the southern flank of The Peak.
Here's the reminder.
Look carefully at the buildings in the distance. If you are knowledgeable of this area you should be able to recognise a few. The two-tone house (orange top, white bottom) is #33 Magazine Gap Road. These days it goes by the name of the Pink House - because it has been painted that colour - and is staff quarters for expatriate senior staff at HSBC. For a closeup of how it used to look, as you see it on screen, Andrew tse has an excellent picture of it on his wonderful FLICKR collection.
In front of it is another building still around - #27 Magazine Gap Road. Gwulo has a few more pictures of this and some extra info here.
Anyway, the fact that we can see these buildings, and the size of the gap between them indicates that we are on Peak Road. I believe - although I can't confirm - that the entrance we see on the left on the screen grab is the entrance to #56 Peak Road. It's changed since 1955 of course, and the hedgerows and trees have grown so much to obscure the view to the Pink House, but here is what the road looks like today, courtesy of Streetview.
There is a similar view still available from the road if we move forward a hundred metres or so, so that we are level with the petrol station. The angles on the buildings aren't quite perfect but at least you can see the general area and, surprisingly, many of the same buildings in the background.