6 month delay on claim from other insurer....

Last July (2013) my handbrake failed and I rolled into my neighbours car. I immediately told the owner and asked her to let me know the cost of the damage as I would rather have paid it myself than go through my insurance if I could afford to. As the car was a Motability vehicle my neighbour told me that she could not get the work done at a private garage but had to send it into a specific Motability garage to ensure the structure of the car had not been damaged. Around a month later I received a letter from the Motability company asking for my insurance details to make a claim. I called the company and asked them again to let me know the cost of the work first as I wanted to try to pay it myself. I have heard nothing since.
Today I arrive home to a £700 bill with 14 days to pay. I cannot afford this so am now going to have to go through my insurance.

Any advice would be great on how long the claim can go on for and whether after 6 months the company can be demanding the money within 14 days? Also, will my insurance company pay up now that it has been over 6 months since the accident occurred?

Thank you