Hi, this is Jim, thank you for the question - I will resolve this for you.
Sorry to hear of the issue. The absence of a signed contract is not an issue as a contract can be written, verbal, or even implied by conduct. However, a written contract is desirable so the parties know the terms they are working to and it certainly helps the court if and when a dispute arises.
In terms of the non-payment, clearly they are in breach of the agreement by not paying you. You are the aggrieved party here. They are being unreasonable in not paying you and saying that they will now engage someone else to finish the job. It also sounds like they did not really comply with the expectations under the agreement they had with you either - that in itself would be grounds to terminate the agreement and demand your payment from them. I do not see how they have a case against you - it is the other way around from reading your question.
I would recommend that you send them a formal letter before action to demand payment within 30 days and say that if they do not pay you what you are owed, you will issue county court proceedings against them. See attached template as an example of what to say. Please let me know if you cannot see the letter which I have uploaded. You will need to tailor this letter to your situation. It should say that you claim your money back due to breach of contract on their part.
You will need to register at www.moneyclaim.gov.uk so that you are ready to issue the claim in the event they dispute the claim and do not pay you. The website is very user-friendly and you would not need a lawyer to use the money claim site. Claims with a value of under £10,000 are classed as a "small claim", so legal costs are not recoverable and the matter may be dealt with on paper by a Judge, not at a hearing. A hearing may be necessary if the court thinks that oral evidence is required to dispose of the case.
Claims between £10,000 and £25,000 are subject to fixed costs only so if you lose then the risk is minimal. Further, the money claim website allows you to sue for an amount up to £100,000.
You would claim the sum for the loss, the court issue fee (details of the money claim fees are listed here at page 5:https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/904862/ex50-eng.pdf) and court interest which is 8% calculated on a daily rate from the date of loss to date of court judgment, plus the Bank of England base rate (under the Late Payment of Commercial Debts (Interest) Act 1998). The site allows you to calculate the interest and add it to the claim. If a hearing is required then there is a fee for this too - see page 7 of the previous link for details. Again, that fee is recoverable if you win.
If you win then once you have the CCJ from the court the defendant has 14 days to pay in full. If they do not then it gets registered with the credit agencies after 30 days. You can also enforce the CCJ with the county court bailiffs or transfer the debt to the High Court for a small additional fee assuming the total amount owed is at least £600 and you can use the high court enforcement officers who have greater powers than county court bailiffs. The transfer fee is added on to the debt and payable by the defendant.
There are other enforcement methods which I can help with, including bank account freeze, charging order on their property (and then apply to force a sale), application to wind up the company if £750 or more is owed (if suing a limited company), apply to summons them to court for questioning, all of which can ensure you are actually repaid the money.
You may find they just pay you after receiving the letter before action – hopefully they will want to avoid litigation.
I hope this helps and answers the question - please feel free to ask me anything else.
Have a good day,