My suggestion would be to pay what you agreed to pay and if the person wants to argue over the rest, then have the argument, in court if necessary.
Whether the person is entitled to payment for the extra work or not would depend on whether that extra work was envisaged when the initial estimate was given.
A little bit more, to my mind is a couple of hundred pounds tops, not double.
I would suggest that you decide how much you are going to pay and let them have a cheque for that amount telling him (in writing) that it is in full and final settlement and that if he does not accept it in full and final settlement he should return it to you and you will thereafter have an argument.
Thinking about it, it would probably be better if you sent in 2 cheques, one for GBP650 which is the original price and the other for GBP200 or thereabouts which is the “extra”.
What you don’t want to be accused of is refusing to pay anything at all.
In your covering letter it needs to be marked Without Prejudice Save as to Costs and then he cannot produce it in court as any kind of admission that you owe anything extra at all.
I would be very surprised if he didn’t cash the cheques and put it down to experience.
He may return the GBP200 to you, saying it’s not enough and it would then be for you to decide whether you want to pay more of him to decide whether he wants to take you to court.
Thank you for letting me assist you with your legal question. I am glad that I was able to help.
I am not certain whether that answers the question for you or not, but I am happy to answer any specific points arising from this.
It will be my pleasure to help you again either further with this or any future questions you have