Hello Paul,
When I first started this reply, i hadn't realised it woudl be so long......
There are some companies that will move caravans but they tend transport rather than tow, and they are aimed more at statics rather than tourers. Google "Caravan Transporters" to find some names - even at least one in Telford.
Whilst none of the national breakdown recovery organisations will help unless there is a breakdown or an emergency, if you have noticed some of the organisations actually use local garages rather than having their own dedicated recovery vehicles, so if you were to actually contact the garage direct (i.e. not through the recovery organisation) they may possibly be able to quote for towing or transporting for you.
Other people you might try. If you are a member of the C&CC, they usually have local groups and possibly one of their members may be able to offer assistance.
Also if you contact your local Scout group, there is usually one of the Scout leaders with a LR or other large tow vehicle, They may be prepared (Excuse the pun) help.
Could be a local private hire taxi service. They may have a drivers who would be prepared to tow. Or you sometimes see a local van with an man for hire.
Local second-hand car suppliers often use individual drivers to collect stock, the dealers may be able to put you in touch with suitable drivers.
I would advise you check out insurance very carefully, as your insurance may not cover your caravan behind someone else's car.
Also I do see a possible issue with the method of delivery. If you were to use your car and hire a driver, the driver has got to be able to get back from the destination by some means, Equally if you use the drivers vehicle, then they will have to make twice the journey as they still have to go home, and come out again to collect you. Its already been pointed out that virtually all these people will probably charge by the mile, so its not going to be cheap.
I wish you good luck.