Staffordshire and the West Midlands may well have many attractions but they don't include mountains ;-)
For the 'real thing' you'll need to travel to somewhere like the Peak District but, for a taster, there are several indoor climbing walls in the area. The Creation Climbing Centre,in Birmingham, is purpose built. A 1� hour taster session costs �20:
http://www.creationwall.co.uk/taster.htm
A 2 hour 'Introduction to Climbing' course costs �35:
http://www.creationwall.co.uk/2hrintro.htm
The 4 hour course seems to be better value, at �49:
http://www.creationwall.co.uk/4hrintro.htm
The main web page (with links to directions, etc), is here:
http://www.creationwall.co.uk/
There's another purpose built centre, Wolf Mountain, in Wolverhampton, which offers similar courses. However, the prices aren't quoted on their website. You have to phone for details:
http://www.wolfmountain.co.uk/
Chris