I should add that there's one other caveat. Sorry if this is obvious. It isn't really a problem with 700c wheels per se, the issue is with rear triangle spacing, - the space between the dropouts in the rear.
As more gears have been added in the back, the spacing has gotten wider to accommodate them. Today 130mm is common for road bikes. Back in the 80's it was 126 and before that it was 120. If I'm wrong about the particulars I'm sure someone will correct me.
Anyway when replacing the 27" rear wheel, it's very likely that a brand new 700c rear wheel won't fit between the dropouts. Steel bikes can be "cold set" to allow the wider wheels to fit. Sometimes you can just jamb them in there but it makes fixing flats an extra pain. Modern wheels use cassettes too and 27" wheels typically used freewheels.
Getting an older set of 700c wheels, which is maybe what you were intending, may allow you to get around this problem as long as they were designed for the same number of gears as your current wheels.