700C wheels usually fit fine on bikes meant for 27". I'm going to assume you were already planning on getting a new wheelset, instead of just putting 700c tires on 27" wheels, which clearly wouldn't work.
A 700C rim's diameter is 8mm less than a 27" rim, so your brake pads will need to be dropped by 4mm. Just measure how much adjustment room you have on the pads, and if you have at least 4mm worth, you'll be fine. Its rare on those older bikes to have calipers that don't have enough adjustment for 700c wheels, but it does happen.
Most of the older bikes came with medium to long reach brake calipers anyway, so going to a 700c may not even require different calipers just a readjustment of the pads-to probably their limit. Easy enough to find out just go to an LBS and have them put a 700c rim on to make sure.