A parking charge results from breach of contract, so either you did not pay when using a car park, or you did but you over-stayed. It sounds like you did not pay within 10 minutes of arriving. You say you have paid but I presume you are now being asked to pay the debt collection fees too. The car park should have a sign clearly displayed with the terms of parking. If you did not see it, they will still have a case against you though what goes in your favour is you did pay and they have not suffered a loss to speak of. So you could contest the further charge - it would be up to you whether you do this. If you do, you may be pursed in a small claim though they are easy to deal with, no lawyer is required.
You will continue to receive letters from the debt collection company if you do not pay.
Debt collectors are not bailiffs - they have no powers as such. They will simply try to collect the money their client thinks you owe. You can turn them away if you dispute the debt and they visit you - they can’t enter your home and take goods. They would report back to their client they were unsuccessful and it’s then up to their client whether to take matters further.
They will send a letter before action to you if their debt collection attempts fail - which is required under the pre action protocol to give you the chance to avoid court action. They usually give you 14 days to pay before they will take civil court action.
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.
You should not ignore the court papers as if you do, the claimant will apply for judgment in default meaning they win and you would not be allowed to defend the claim.
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.
If the claim has no merit then you have an option (after your defence is filed) to apply to strike the claim out. The court will consider an application if the claim has no merit, or is misconceived.
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.
But certainly I think you would succeed in a defence, just to be clear.
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.