Greetings Mathsgeek and welcome to the forum
Found this info on my travels :-
Q. If I take my CBT on an automatic bike, am I allowed to ride a geared bike?
A. Strangely yes but we would recommend getting a couple of hours training with us on geared bike operation.
Q. Do I need to do another CBT to move from automatic to geared machines?
A. No, as long as the CBT is in force there is no need, but we do recommend that people upgrading or moving to geared machines have further training.
There was no reference to the source of this information which is why it's not on this forum, so I suggest that you check it out with a riding school first.