Unless your terms and conditions allow for a refund then you should refuse. The client entered in to a binding contract with you. If they want to cancel then you would be within your rights to retain the money paid. The pandemic has impacted many contracts - some to the point they are void due to "frustration of contract", meaning the terms are impossible to comply with. Some contracts have force majeure terms, allowing the parties to pause the contract due to the disruption. You mention you were were given an extension. The client cannot cancel in this situation.
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.
If the claim has no merit (my view is, subject to considering your terms, their claim if they make one would have 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 application costs £255 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.
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/