It is normally a term of a car insurance policy that you must notify the insurer within 24 hours of any accident, no matter how small. If you don't then you risk them cancelling your policy or not paying out if there is a claim. You cannot pass that letter to your insurers as they will tell you they will not cover you. You say that you hit the car so my view is that they will win a claim if they make one against you. You will need to consider making an offer to them, or defending the claim if they sue you - but your defence needs to have merit and solid reasons of why you dispute their claim, otherwise they or the court will strike it out. Meaning they will win shortly after you file a defence but it would buy you a few weeks (as when they apply to the court it will take a while for the court to list a hearing). You would reply to the lawyer to say you have no money and assets so it'd be pointless suing you. You should reply to them to say you want more time so you can take legal advice - they may hold off for another week or so.
If they do sue, you will receive court documents (a response pack) which you must complete and return to the court. It is a tick box exercise for the most part and there is a short section to write a defence which is easy enough though please feel free to come back to this site if you need any more help. A claim will also take 9-12 months to be decided at court. If you lost then you would get 14 days to pay the judgment before the claimant can enforce the order, and 30 days to pay in full before it is registered with credit agencies. The claimant cannot recover legal costs if they win, in a claim under £10K (a small claim), all they can claim are the court fees and interest.
The hearing (if the case gets that far) is likely to be held remotely, it's you, a district judge (who is a practising solicitor or barrister) and someone from the claimant company. The Judge decides and if you lost, you get 14 days to pay the sum. If paid in full within 30 days then nothing goes on your credit record.
If you lost and if you were unable to pay the full sum owed at that point you can also ask the court to pay by instalments (a simple form is sent in, form N245, and a fee of £50 unless you qualify for a fee exemption so if you are on a low income, have low savings or in receipt of benefits then you would qualify). If the CCJ was not paid in full though bear in mind the credit record would contain the CCJ details for up to 6 years. After that it comes off the credit registers.
I can assist you going forwards if it gets to the point they issue a claim. If you need a law firm to assist you to defend the claim, here is an example for you and they offer a fixed fee : https://stormcatcher.co.uk/practice-areas/dispute-resolution/small-claims-lawyer-service/