You may have some luck at the Yorkshire Flight Centre (if I recall the name correctly). Based near Knaresborough they have a B737 that is used for joyrides although I have no idea of the cost.
I got the details from BT Directory enquiries on line - please note that I have no experience of this place and am not endorsing them, or any one else!
Yorkshire Flight Centre
(01423) 340664
Moorhouse Fm, Moor La
Arkendale
Knaresborough
HG5 0RQ