How can I know what the tradesman says is really done?

Hi I have a property in Bishop Auckland and I am based in London myself. I advised my job here and one tradesman contacted me and on the phone and based on the pictures he quoted us £3000. This quote was cheaper that the £4K quote that we had received from our managing agent so we agreed to meet him at the property to ensure that he can finish the job in the agreed time frame and also he sees exactly what is going to do. When we met him, he came across a very genuine guy and after going through details of the work expected he still confirmed that the cost is £3K and he will finish it by Thursday (5 days later) . We cut the keys for him and asked him to start the job. He said that he needs 50% of the payment upfront before he starts but he is going to send us an invoice. On our way back to London on same day, he emailed us the quote but we noticed that he added VAT to this amount which has actually increased the cost by £600. We got in touch and informed him that this is not what we understood when we met him as at no point he mentioned that the price is excluding VAT. Because we had already left him with the keys and his price was still cheaper than the other quote we had, we agreed to make the payment after he offered £300 discount on the £3600 he invoiced us. Two days later, he contacted me and said that there is a serious issue with the electricity and the radiators are leaking in the house which he is fixing at the moment. He never informed us about the details of the issue with electrics and he just said that he would amend the invoices for additional job. We have now received the amended invoice and he charged us £612 for this additional work which I feel is very excessive, I have full home cover with British gas and I could have got the issue fixed through them but he fixed them before he gives us a chance or even tells us how much he was going to charge which I feel is very unethical, unprofessional and cheeky. He hasn’t provided us with details of what was wrong and what has been done to fix it and a form of assurance that the fix is done by certified people and it is guaranteed. Can we ask him to provide with these details before agreeing to the amended invoice or not. We are not there so we can check what he is referring to because the property was rented before and we never lived there ourselves. Would you please advise on what would be the best course of action?