Thanks for the tip about brakes – I imagine that would be a bit of a pain.
If it's not too daft a question (well as I don't know the answer it's not the question that's daft, just the questioner).
What measurement am I looking for when I check the wheel rim profiles to see if they match?
I think the safest thing would be to actually try a would-be new wheel in the bike and see if the brakes were still aligned properly! Not much use if you are buying them mail order, unless you can try a mate's wheel first.
I mentioned that to someone else and he reckoned that one of the two pairs of wheels that I used must have been very strange because in his opinion, most wheel rims are the same profile.
I must admit, that pro riders don't seem to have a problem when they get replacement wheels from neutral service.
I think you'd have to ask someone who knows more about this subject than me. I just know that I had the problem and am flagging it up! I hadn't given it any thought until I got it wrong.