I would relax about this. The law is on your side for two reasons.
Firstly I suspect they have not sent you an invoice? If they have not sent you an invoice they can't easily take any action through the courts to enforce the alleged sum owed. If they have sent an invoice query it and ask for a detailed and costed breakdown and simply state that the invoice rendered is unrelated to the verbal quote that you have received. Yes, it should have been a written, emailed quote, but that is water under the bridge now. Also if the 'invoice' doesn't state the company registration number and their VAT number query it on that basis. If they claim to be VAT registered the invoice must have the VAT No on it. Then check the VAT number relates to the company on the gov.uk site
https://www.gov.uk/check-uk-vat-number.
Secondly, as one of the other posters has said, if they turn up at the house call the police. If they try and rip their work out then it is a simple criminal damage. The law is very clear on this wrt to domestic building works that once goods and materials are affixed to the house/premises they cannot be removed without the building owner/lessee's consent.
I would be careful of becoming a cowboy investigator and starting to recored conversations as the recording may well not be admissible in proceedings as they were covertly obtained. But, I would keep a hand written contemporaneous diary of that is said by whom when.
To take control of the situation, what I would do is to ask for a breakdown of the purported costs and how they are calculated to be delivered up in writing within seven days for your consideration. Do it by email. I would then go back with a reasonable offer of settlement which is in line with their original quote and show a simple, fair and clear calculation of how you have arrived at it. For instance if they gave you and hourly rate card for their workers beforehand you have to use those prices. If they show you an invoice for materials, cross check them online, but you are probably stuck with those costs even if they are, as an example 40% OTT, because that was what they paid actually for them.
I wouldn't waste money on a solicitor at this point. Keep it simple and report back how it rolls.
Good luck.