Locations of, and contact information for, hair salons outside London
where 'Yuko system' is used?
(Also known as 'thermal reconditioning' this is a new
straightening/treatment system which originated in Japan and is
becoming increasingly popular in America. I know it is available at
Curzon Street, London and also Harrods but am looking for somewhere
closer to home - West Yorkshire. It has been suggested to me that a
Salon in Sheffield uses it, but I can't find any more information).

Couldn't locate anything right off outside of London, could only
confirm what you already knew about.

There is a website--> http://www.yukosystem.com click on the English
version link

That'll take you to a website for the US, but it mentions the salons
in London that use the technique and has a 'Contact Us' area where you
might be able to solicit the info.

Also, you could try contacting Harrod's http://www.harrods.com/ and
seeing if they knew of anyone outside of London doing the procedure...

There is one in Shrewsbury:
http://www.rainbowconnectionsalon.co.uk/location.html

I had it done with Christian from Exhibit, I  already had it done
somewhere else, but never been so good like now.I'm glad I decided to
come to London and see him (I'm from Oxford). His website:
www.go-straight.com