@Alan Edgar (Eggy1948) @Justine MatchettLooking at those two photos, Alan, I think they show exactly the same buildings with Milburn House first on the left. I've had another think about the location and today I've compared OS maps with the enumerators route on the 1901 1911 and 1921 census returns and also the 1939 register. I'm now inclined to think that Garden House maybe still exists and could be the white house (albeit renovated or even rebuilt) immediately behind the bungalow adjacent to Milburn House.
Looking at maps I can see that there has been a building on that spot, immediately behind the Railway Tavern (formerly Railway Hotel then Railway Inn) since the 1860s. Here's a map from 1898. I've arrowed the building in red:
The map below is from 1924 (simply because it has the best detail). The Railway Inn I've arrowed green. What I believe to be garden House I've arrowed red, and I've arrowed an L-shaped building to its rear, on the same plot of land, which I'll come back to. Note that the present day bungalow isn't there. That corner where it stands appears to be land belonging to the house.
The Railway Tavern is now demolished to make way for the new car park but the side street behind it, leading from the main road and giving access to the two buildings is still there. I had a little wander down that side street (with the help of Google) and I could clearly see that the L-shaped building is still there and seems to be very old.
If William Graham, Benjamin's father, ran a carting business and later a market gardening business (at his home address, according to the 1921 census) then that would be the ideal place - maybe stables for horses when he was carting.
The name Garden House, from 1911 when William was a carter, may well be a topographic name - referring to the fact that it was the only building there with a garden which faced the main street. making it easily identifiable. Look at the old maps and you'll see that all other buildings had a back yard and/or an allotment garden along the length of what is now Melrose Villas and Melrose Terrace.
All in all, the census returns show that the Graham family have lived on the same spot between the Railway Tavern and, after its construction, Milburn House. From 1911 it had the address Garden House. On early maps this is the only house adjacent to the Railway Tavern.
What do you think? Could this be Garden House? Anybody living in the area today who fancies knocking on the door and asking? I'd love to know.