I posed the question on The Historic Coventry Forum regarding the original HR road sign and a forumite kindly responded as follows ......
I could be wrong but one of the original Highfield Road signs may have gone before 1937. Stepping through the maps, the east side of the street used to have about 4 more properties on it. They were demolished to extend Thackall Street. Instead of a road, there was a footpath leading to allotments and on to Swan Lane. It seems reasonable that the Highfield Road sign was on the first of the demolished terraced houses as it would have faced travellers as they approached the corner. The west corner doesn't have its full set of decorative brickwork on the ground floor and looks like it might have been a shop at some point. The sign, if there was one, could have been removed when it was turned into a shop or when it was converted back. There don't seem to be signs at the other end either. They may have vanished due to renovations to the buildings (eg rendering) or to a light fingered fan. The sign at ground level on the corner in Google Street View vanished between 2020 and 2022.
Another forum member chipped in with the following.......
The corner house in question was a general grocery shop which was run in the 60's -70's by Jack Patience. If my memory is correct he was at that time the chairman of the Coventry City Supporters Club which was housed under the stand opposite. The entrance to the shop had a corner door entrance, common to shops of 1920's build and large windows to both sides. There was a bomb site on the opposite side of Highfield Road and on match days there was a man who sold tickets to look after bicycles which he charged around 3d per cycle. A couple of my mates lived in Highfield Road and I can remember being chased of the allotments several times as there were a couple of apple trees on them which backed onto Ranby Road and were accessed at the other end of the street........happy days