Leiceister used to have one night a week and from what I remember we were only ever charged for the one circuit,no idea how much as it was the student who payed.Great for night flying as the ground lighting(i.e from homes) isn't huge so it good experience for the student.
Wellesbourne had a similiar set-up but I used Coventry most of the time who were expensive but very heplfull turning runway lights off etc and even using the light gun when it worked!They would do the odd SRA if time permitted aswell.
Liverpool will I've heard accomodate night flying but as with Coventry you will have to work around the commercial traffic which can mean lots of orbiting. I always found that the Coventry area was quite good as you had Daventry and Honiley vors to use for the Nav with just enough traffic about to make it interesting without been to much,although it was closed I always got the student to try and find Sywell,not so easy in the dark!
Hope that helps.