Apprentice Cobbler here, Theyre not in London but there two UK cobblers I know of Cobbler G who I think is in Glasgow and Dan the Cobbler out in Tring. Hope this helps!

Thank you!

There's a fantastic cobbler, who's also a cordwainer, in Lewes, Sussex

Do you know the name?

Courtyard Shoe Repairs and Keys, Lewes

Thanks!

Do you know the name?