Well hurrah, finally we get there...I hope I'm not going to have to ask every question 3 times before you answer, or I might lose interest.
As he was in your house when you agreed to the work, the contract formed between you is known as an "off-premises contract". In other words, the contract was made away from the trader's premises. This means you have a legal right to a 14 day cooling-off period, during which time you can cancel all the work and demand a full refund. The 14 day period is extended up to a full 12 months if he does not inform you of your right to the cooling-off period in writing, and only reverts to 14 days once he provides you with this written advice of your rights, starting on the day he provides you with such advice. You are not required to give any reason for cancellation. They will be entitled to recover any materials supplied to you so far, if they so wish.
As it's a Ltd company you're dealing with, your contract is with the company, not the individual who visited your home. As such, you can start proceedings against the company, beginning with sending them a formal letter requesting cancellation of your contract under the terms of the Consumer Rights Act 2015 and a full refund. State that you are happy to arrange for them to collect all materials supplied to you once they have confirmed the cancellation of the contract. Also give them 14 days to respond, and advise that if you have not heard from them within 14 days you will commence court proceedings against them. You should send this by Recorded Delivery, so that you can prove they have received it. Also photocopy the piece of paper he sketched the plan and payment schedule out on and send a copy of that with the letter. Until such time as it's proved otherwise, I would suggest you assume that the company whose details Denso linked to earlier are the company you are dealing with, even though they are in Lutterworth and you are not. It's not unusual for traders from other areas to travel to London for work.
Once you've done this, wait to see what their response is. What they say to you will guide your next move.