G-T
Most personal injury solicitors will pursue a claim on a 'no-win, no-fee' basis (This means that they only undertake claims which they hudge are likely to be successful. They anticipate recovering your costs from the other side, and if you lose, they stand the costs as the result of their own poor judgment. To avoid you being liable for the other sides costs if you were to lose, they take out an insurance policy, and the cost of that policy is either recovered from the other side, or the policy pays out to pay for itself. All clear?) It's best to pick a solicitor with some expertise in cycling matters. Several advertise in the cycling press. The CTC soliciotrs Russell Jones and Walker, one of the biggest personal injury solicitors in the country, trades on the internet as Claims Direct.
http://www.claimsdirect.co.uk/ No need to be a CTC member to use them. Action of this type leads to a claim for compensation, not punishment of the driver.
If you do decide to go to a solicitor, do so immediately, not months down the line. As others have said, you can negotiate directly with the driver's insurance company but I'd advise against that. You have no idea what would be a fair settlement of your claim. Insurance companies are notorious for bullying and dragging their feet, especially when dealing with members of the public. They will not mess about if approached by a solicitor, partly because they know that solicitors' fees operate like the clock on a taxi so prevarication and procrastination cost them £££.
I'm a bit unclear about the circumstances - witnesses calling an ambulance but the police preventing you from pushing the bike when you walked home.
Witnesses can be very fickle - shouting their mouths off at the scene then melting away when police notebooks come out. Many of those who shout loudest have often witnessed nothing - they've heard a bang or similar then put 2 + 2 together. OTOH, if the police don't even try to investigate, then it will never be anything more than your word against his. There has been a trend for many years for the police to investigate fewer collisions and I'm not sure what the current criteria are.
If you are unhappy about the way the police have dealt with this, you can always complain. You can now even do this on line:
http://www.ipcc.gov.uk/ Before you do complain, spend a bit of time identifying what you feel was done wrong eg inadequate investigation which led to independent witnesses present at the scene not being interviewed and their details recorded.