You need to pass your CBT (Compulsory Basic Training) to be able to ride a 125 cc bike.
As you obtained your car licence before 1 February 2001 you do not need to complete a CBT to ride a moped (a moped has an engine not over 50 cc with maximum design speed not exceeding 50 kilometres per hour (km/h) which is approximately 31 miles per hour)
Do it sooner rather than later as the bike tests are changing in, I believe, October 2008 when it will be more expensive to pass your bike tests, be harder to do so as it's more involved (although you could argue it'll make you a better rider once you've passed the part of the test that allows you to ride any size of bike), and there'll be less training / test centres (there will be more emphasis on learning to ride at specialist centres before they let you loose on the road ... this is my lay-persons understanding). Have a lookat www.dsa.gov.uk for more info about CBT, bike training and the new tests