I had it at the back of my mind that there was an old tool dealer in the Lake District but had not bookmarked it. I have now found it -
http://www.johns-tools.co.uk
He does not have a shop but travels round to many antique fairs and similar events, listed on his website, so maybe one will be in the right place at the right time for you.
You mention that the references for tool shops in London are a bit old - I've never found any specialist outlets, but presumably some tools would turn up at general markets such as Brick Lane or Portobello Road. Following on from that thought, I checked the website for the Portobello Road antique traders association -
http://www.portobelloroad.co.uk/specialist.asp - which lists:
"Bygones":
Specializing in wood working tools, historical aero- nautica, clocks and related items. Also optical instruments, compasses, fishing artifacts, pond yachts, bowling balls and general items.
Contact David.
Outside Admiral Vernon, T4.
Tel: 01727 860753
Mob: 07830 250077
Email:
[email protected]
so maybe that will be worth a look.
Have a great trip, but be sure to take some photos and report back!