737 Sims
For 737-200, two options spring to mind:
The Flight Centre in North Yorks. (under new management, a very helpful and experienced ex-Cathay pilot; you won't need a buddy as he controls the sim from the other seat), or
The sim at Parc (Dublin airport) can be booked independently with an instructor
For 737-300/400.. try Melissa or Edward at IAGO Solutions who will book you in to a GECAT sim at either Gatwick or Heathrow (Stockley), with a TRI. They'll need ID and a copy of your licence.
However, if you just want general jet handling at a fair price then there is a 727 at Bournemouth. Mike Bolton is the man; he advertises in Flight.
Other than that you could try Oxford ..