There's a few hundred likely places in Kent. It's not a difficult job for a true shoe repairer though some kiosks might shy away because it involves a bit more than just glue and a quick buck. In the latter years of my old fella being a shoe repairer (20 years ago), he used to resole army boots in his own time at weekends and evenings. His boss couldn't justify doing them during the normal working day because of the time involved (half an hour, rather than 5-10 minutes) and the cost that would have to be passed on, so the customer would get them repaired for little more than the cost of Dad's overtime. While his boss wasn't seeing much profit on the boots, he banked on the customer and his mates coming back with their civvy shoes.
20 years ago, I would have vehemently disagreed with you because at the time they were probably responsible for ruining more stitched-sole shoes than they repaired. They had all-in-one repair-anything machines operated by an oik who'd had a half-day lesson in using the machine but no education in repairing shoes. I wouldn't have trusted them with anything more than a stick-a-sole and even then...
Nowadays, they're probably as good as anywhere - provided you don't need hand stitching and your soles fit their standard sizes. Also they can send the more difficult stuff away to be repaired. They've greatly improved. So for a first repair, they're probably OK, but I'm not sure I'd go there for the second and subsequent repairs.
If you anticipate your boots needing more than one repair in their lifetime, I'd advise going somewhere that hand stitches so the thread goes through the original holes in the upper. Machine stitching will create new holes, eventually weakening the leather like the perforations on a sheet of stamps.
Fair play to the bloke for being honest if it was outside his comfort zone. Better to say you can't do it rather than **** it up. You either fix it properly or you destroy it. Perhaps the most annoying thing to happen is that you produce a really tidy job but it squeaks because you didn't check that the other layers were intact when you had the sole off.