Cub Air at Redhill had a Tiger [1] la couple of seasons ago but I'm not sure if they still have it, although I did see it overhead at least once last summer. They also do tailwheel conversions on, well, Cubs......
[1] G-ANDE
http://www.cubair.demon.co.uk
Cambridge Flying Group however definitely have Tigers for training.
If you would prefer to fly during the week you should contact Betty Ison on 01223 293343) to make a booking. For weekend bookings the contact is David Kirkham on 01763 220255. You need to bring warm clothes (even in summer). The group has helmets and goggles.
Current membership fee is £ 85 per year. Depending on your progress with the conversion to flying a taildragger you should be able to fly solo after a few hours with an instructor.
To get to Cambridge Airfield, drive from London to Cambridge on the M11, leave at exit 11 into Cambridge, follow signs to A1303 (Newmarket Road) or Airfield if signposted. The gate to the Flying Clubs is on the right hand side (coming from center of town on Newmarket Road). You pass a large car sales place on the left and just after that on the other side is the gate. If you pass a petrol station on the left, you have gone 200 m too far.