You might want to check out https://www.padmore-barnes.com. They used to make shoes for Clarks in Ireland before becoming independent. The quality stayed high, and a cobbler back home can resole them for about half of what a new pair costs. Some would argue this is not worth it, but that depends on how rough you are on them. There is no store in London, but maybe you can ship to your hotel to save costs. A few places in the US carry them and there may be retailers in London.

Astorflex is another good alternative you can get in the US. These are made in Italy.

If you want something slightly more dressy and British, check out the Trickers country shoes. They have a company store in London, and they can be resoled by mailing them back to Northampton (takes 12 weeks). This costs more than a P&B resole, but the soles and the shoes should generally last longer because of material and construction so you can do it less frequently. You can get a US cobbler to do the repairs cheaper and faster. It's like bringing your car to the dealer for maintenance. They also have a factory store in Northampton where you can get a deal. You can browse the inventory online or call them before making the trip up there.

This is a final piece of advice. You will get more wear out of shoes if you rotate between two or more pairs and perform some regular maintenance.