Thanks for your question. My name is Greg and I'm going to help you with it.
Firstly, it sounds like you have received a "letter before action". This is pre-litigation correspondence that should set out a summary of the proposed claim, calculation of the sum claimed, evidence that the claimaint intends to rely on and a reasonable deadline for response.
It's imperative not to ignore a letter before action and if you need more time than has been offered or require more information on the claim, reply stating this and provide a reasonable time when you expect to send a full response (14 - 28 days from receipt of full details of the claim is typical).
Your full response should either deny the claim in full, accept it in full or accept it in part (and deny the rest). If you believe that certain services have been provided to an acceptable standard and should be paid for, you can accept them and apportion this accepted part of the financial claim appropriately (including details of how you propose to make payment and that it will be in full and final settlement of all claims arising out of the subject matter of the proposed claim set out in the letter before action). If you are going to accept anything or make any offers, the letter should be marked "WITHOUT PREJUDICE".
As soon as possible you should also start collating evidence to rebut the claim. Don't spend too long trying to prove a negative as it is for the claimaint to prove his case on the balance of probabilities. So if he hasn't done something, put him to proof. However, if you have evidence that clearly shows he hasn't done something, this will be useful. Witness statements, screen prints, emails etc. are all useful and admissible.
In the absence of a formal written contract, the oral evidence of the parties and any correspondence will be key in showing what was agreed. Once the terms of the services and the price have been agreed (or determined by a court), the question will be whether the service provider discharged all of his obligations and whether, in doing so, they met the implied terms required under statute (i.e. that they were provided with due care and skill, within a reasonable time etc.). If he failed to do either, it is likely that he will be in breach of contract and he will not succeed in his claim for all or part of his fees.
By way of process, if a claim does end up being brought against you in the county court, amounts under £5,000 are dealt with in the small claims court where costs for bringing/defending the claim are fixed (and relatively small). This means you can't recover large sums you spend on solicitors defending the claim (unless its particularly vexatious) and, on the flip side, you won't have to spend a fortune on the other side's legal costs if you lose. The reason I'm pointing this out is that most small businesses will take a view on how much professional legal services that want to obtain on a claim of this size.
Please don't hesitate to let me know if you need any clarification on the above information and best of luck.