TTN,
The answer to your question appears to be yes. If you look at this website:
Ronaldsway Air Traffic Control in the 1940s
there are lots of pictures of ATC towers, if you scroll down about two thirds to the section on RNAS HMS Urley, you can see images of the RN tower, which appears to be a standard 4 storey building as per the programme and the image in post 5.