Oh, he turned up 5 minutes later and (eventually) got the wheel off with mallet and penetrating oil. It's a little annoying that we had to call him out, a mere 6 miles from home. It's more annoying that the tyre is totally mangled, but that's what happens when you drive on a low profile tyre for any distance when it's deflated.
Ah well, £100 for the tyre replacement. But money is not a worry for us these days, and for that, I'm very thankful (having been through "how the hell am I ever going to get out of debt").