Agile said:
It all depends on the cause of the disagreement which you have not bothered to explain to us.
And you have not "bothered" to ask.
Certainly they can stop working if they choose to and they can claim payment for the work done to date.
It isn't that simple. If the contract was a completed job, then it's a breach of that contract not to complete it.
I appreciate that there are some firms that do a very poor standard of work and they are unlikely to be members of the Institute who have a complaints procedure.
And a fat lot of good that would do anyone who lives outside cloud cuckoo land.
Unfortunately as you seem to think that you can force them to walk out and that you dont need to pay them for the work they have done so far that makes you appear like a cowboy customer who wants work done but you just dont want to pay.
That's an assumption.
You should have insisted on a written quotation detailing the way the work was to be done and the firm should have insisted that you signed the quotation as accepted before starting.
That's your opinion - there are many happy traders and customers who operate without anything in writing.
It will also be more difficult for you to get anyone to finish the work as you will have been tagged as a non paying customer who wants something for nothing.
Tagged? WTF?
__________________
To the OP, you might not have a written contract, but you have a verbal one and it
is legally binding, it's just harder to prove what it comprises.
If you make working conditions untenable for the trader, e.g. by being what they think is unreasonable, then you've both reached a point where they can't really continue. Whilst you'd be within your rights to hold them in breach for not finishing, this would just end up in a big bun fight, i.e. wasting resources with no clear winner.
If things have gone too far, then the sensible thing to do is agree to cancel the contract, agree an amount to pay them for the work done, and then get someone in to finish it.
On the other hand, you'll struggle to find someone willing to pick up an unfinished job - it's never a very palatable proposition for any trader.
This means that the best advice was that given by croydoncorgi - rebuild the bridges and find a compromise.