Sorry to hear of the issue.
A case like this concerned breach of contract - you use a car park which has restrictions and you enter in to a contract when you do. You are then liable to pay to use the car park - if you don't, or you and you overstay then they fine you.
You say you were not in the car park - they need to prove you were so you should ask them to provide evidence (CCTV footage or stills) to show the date and time they allege you were in the car park.
They should 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.
It is recommended that you reply to this letter given the courts expect parties in a dispute to engage and discuss their dispute, to try and avoid 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 (e.g. they cannot prove you used the car park on the date and time in question) 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. You should first invite the claimant to voluntarily discontinue their claim within 7 days if it gets to this point - tell them if they don't then you will apply to strike out and seek your costs if you are forced to do so. If you have no response or they reply and refuse then you could apply to strike out.
The application costs £275 but this is recoverable if your application succeeds. If you are on a low income, have low savings or in receipt of benefits then you can ask the court to waive the court fee. If you won the application, the claim is struck out.
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, assuming they cannot show you used the car park in question.
I can assist you going forwards if it gets to the point they issue a claim.