How can I replace the wheels on my road bike?

I have a 1970s Coventry Eagle road bike with 27 x 1&1/4 inch wheels. Unfortunately the back wheel is now in pretty bad shape and needs replacing but I am having difficulty finding a wheel that fits. When I had a newer bike I always bought wheels with the reinforced double rims as I am quite heavy and the single ones tend to bend quite quickly. I cannot get hold of any in this size as it is an imperial measurement. I have been told that I can't put a new measurement wheel on because of the caliper brakes. Is there anything that I can do?