Might be worth giving these guys a ring if you want some time in a professional sim. I'm pretty sure they'll have access to a 737NG.
Flight Simulator - Virtual Aviation
Alternatively, there's a 'play' sim at the Bluewater shopping centre (and a few other locations). I've had a go on it and it's alright. It's a pretty good representation of the NG flight deck, so it'll probably help you find your way around the cockpit and practice SOPs. However, because it's MS Flight Sim under the bonnet, the handling and feel is way off, so it won't help with the stick skills. It'll probably work out a lot cheaper as well especially if you can negotiate a bit.
IPilot Flight Simulator Gift Experience - Bluewater, Kent, London, Munich and Dubai