Leaving the sale of goods act and the quality of the timber apart, on these facts, yes they can chase you for the outstanding balance because what you did is not sufficient consideration for them to forego the balance. There is a way of dealing with this. But you are too late to deal with it this way now and you will not make the same mistake again.
There is plenty of case law going back hundreds of years in support of them getting their money back. But, if you read on, you will see what defeats all that case law
I will tell you for future. . I suggest sending a cheque a syou have done Armed with a cheque in the hand for some of the amount they want, compared to an argument over the whole of the amount, (and arguments. They may win or lose) the cheque in the hand is a pretty powerful incentive to accept it.
So consider deciding how much you would like to pay the (you need to make it attractive enough) and send it with a covering letter headed “without prejudice save as to costs”. That means that they cannot produce the letter in court as any proof that you admit owing them any money at all.
Tell them in the letter that you are offering this money in full and final settlement of all claims against you, past, present and future, and that by cashing it they accept it as such. Tell them that if they do not accept it, they should return the cheque to you and if they issue legal proceedings, you will defend them on the basis of A, B, C, whatever.
Tell them that if they do not understand the significance of the letter. They should take independent legal advice.
I can tell you this approach works nine times out of 10, provided the offer is reasonable and not derisory.
For legal reasons which I will not bore you with but which go back several hundred years, the cheque must not come from you, but was come from a third party, friend, relative, solicitor, our accountant, neighbour, girlfriend, wife, husband, whoever, just not from you.
Of course, you may have a claim under the sale of goods act if the material is defective, but you did not raise that issue. If they pursue you for the £2000, you can raise is your initial correspondence as a defence, but don’t bank on it working if the judge knows that particular law. You can of course defend on breach of statutory duty (fit for purpose and satisfactory quality) under the sale of goods act and breach of contract.
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The thread remains open for us to continue this exchange