In reply to Jim Braid:
All done. Moving the tyres into the warmth was the key. Took 3 rounds (2 outside) with the rear wheel and when I started on it inside it went on, well, not easily, but with the sort of difficulty I had expected. Didn't need to use tyre levers but did eventually put on a pair of gloves. Think it helped that I'd already spent a fair bit of time, albeit unsuccessfully, trying to get it on.
Front wheel went on in the first round of trying and again was about as hard as I'd expected. Gloves also used.
Having finally managed it gives confidence that should the need arise I'd be able to get the tyre on and off again.
"... pop in to an old style bike shop for 3 steel tyre levers"
Yes, remember them well from my youth. Are they not a bit longer than the current plastic ones such as Park Tools so more leverage. I think when I used them in my teens bikes were a bit more, well, robust. Not sure that they wouldn't damage modern wheels.
Looked at the Park Tools recommended way of using the tyre lever to put the tyre back on and it is to use the lever the same way round as taking it off i.e. hooked under the tyre. Couldn't get this to work at all. Felt more likely to succeed when it was used the other way round and hooked on to the rim.
Thanks again to everyone.