Just to add, you can obvioulsy pre book one if you wanted but I don't know where you do this. I've never seen dozens of pre booked ones waiting, one or two at most usually. Just ask the driver what name they are booked for to find out if its yours.
You shouldn't have a problem getting a taxi within a few minutes after the theatre - there are usually dozens passing. I'm not sure where the Cambridge theatre is but if it's a bit tucked away then just walk to a busier road and hail one from there. If you still have no luck then wait somewhere near a hotel or station where there are likely to be taxi passing.
Remember that only taxis with their yellow light on will stop (sorry if that sounds patronising but I've seen people trying to stop a taxi without it's light on and getting v annoyed).
Stupid question time - sorry I am taking dd (7) to London to see Matilda for her birthday at end of Jan. We are travelling from Bristol on the train, arriving in Paddington and happy to grab a taxi at the station to the theatre. On the Cambridge Theatre website it says we should have no problems hailing a taxi when we come out but one of my friends said they had a nightmare. Is it worth pre-booking, and if so, who on earth with? Never pre-booked for London before . Now for the really ridiculous question, if there are masses of pre-booked cabs at the theatre, how on earth will we know which one is for us?