Ok, I have done the field trip... Here is a new photo.
They don't seem to be very keen on house numbers or even letterboxes in this street, but fortunately the internet can lend a hand.
Just out of shot to the right is Jack Wills at number 40.
Then there is Cannon Street (which, by coincidence, includes a shop 10 yards in occupying numbers 41 & 42 - Cannon Street.)
Then there is the formerly empty shop, now occupied by Charles Tyrwhitt at number 41.
Then Muji occupying 2 premises, at numbers 40-42
Noitice that 2 of the windows above them also have Charles Tyrwhitt written.
Then an empty shop which I believe to be number 42a.
Then Needless Alley.
Then Tesco, at numbers 43-48.
In summary, I believe 41b was somewhere in the elegant old red building, possibly in an office/workshop 1 or 2 levels above street level.
On the opposite side of the road is Burlington Arcade (same name as an alley in London selling antique pocket watches, among other things, to people with deep pockets) with the Burlington Hotel above it, and at street level a shop selling premium Swiss watches.