Thanks for your comments everyone, glad that most of you agree that I'm not at fault.
Just a small update; I spoke with the British Cycling solicitors this morning on the phone and went through the details and they've sent me all of their forms to fill out. I'm also planning to attend the walk-in centre at my local GP tomorrow morning to get my back looked at because its got more painful, not better. All other soreness seems to have gone away, but my lower back is spasming so I'm assuming some kind of soft tissue injury - bruising or strain caused by the impact.
The solicitor I spoke to seemed to think its likely that the other party would be found liable given the circumstances of them reversing off their drive. Obviously it's down to his insurers to challenge this if he doesn't admit liability. He said I should be able to recover the costs of repairing my bike, related costs like extra travel (although the £11 for my cab journey might be challenged without a receipt) and if I want to persue a personal injury claim, I could be looking at around £500 if I recover within a few weeks (which seems the most likely), more if it takes longer. If I go this route it could take months to resolve, but that's fine by me.
As I said there were no witnesses but between my video of the conversation with the driver where we discuss the incident and the police incident number its very unlikely the driver will be able to deny what happened I think.
I'm going to get my bike back from
Halfords today and see what the result of their inspection was. As advised above, I'm going to take it to another shop for a second opinion and quote - no good local bike shops around here unfortunately however I do have a friend that works at Snow & Rock and they have a Cycle Surgery workshop and I'm happy to trust his judgment, so I'm going to take it to them to be looked at and hopefully fixed.