The ideal person to do an assessment and a report would be a buildings surveyor, but you might be throwing good money after bad.
Firstly, do you have any evidence at all, e.g. an invoice or a receipt, that this tradesman did the work for you?
Secondly, while it is very understandable that you have lost confidence in him, if you don't give him the opportunity to put things right that is going to work against your chances of winning a claim against him.
As suggested, the first thing to do is to take some decent quality photographs of the problems, and get three written estimates for putting things right.
Then I suggest you send him a Recorded Delivery letter telling him why you are unhappy with his work, and relate your comments to enclosed photographs of the problems. Say that you have had the work assessed and quoted on by three other tradesmen, and that the mean cost (the middle estimate) to put things right is: £***.00. Point out that the estimates (not quotes) are based on what can be seen to be wrong, and do not cover any work that might come to light once remedial work is underway. Ask for a reply in writing within 28 days, and add that if the matter cannot be resolved satisfactorily you will consider making a claim against him in the County Court (if small claims track the claim will need to be no more than £5000).
Then see what kind of reply you get, if any.
If he defends his work then at least you will have some written evidence that he has done work for you. He may want to come and inspect the work himself, which you will need to allow him to do.
If he offers to put things right, then maybe you can convince him that you want any remedial work done by someone other than the original person who has made a hash the first time round. Perhaps he has other people working for him who could do a good job, or he might want to sub it out. Or he might agree to make a refund, in full, or in part.
If you can't agree, then you have the option of registering a claim against him in the small claims court, which you can do on line, you don't need a solicitor - you can use a solicitor if you want to, but legal costs are not usually awarded in the SCC because the idea is based on DIY presentation of your case to get justice as cheaply as possible.
If you go to the Court website you can look up the fees, which depend on the size of your claim.
You can serve the notice of proceedings yourself, or the court will post them to him.
How long will it take to get to court - hard to say as it depends on how busy they are, say three months at a guess.
Give him 14 days notice of your intention to register your claim in the CC, because you might find that he has second thoughts during that period around settling the matter out of court.
If it gets to court, then just turn up with your Invoice/Receipt from him, your photographs, estimates to put things right, and explain your case to the Judge. The job quite obviously looks a bodge, and that will go in your favour.
If this guy ignores your letters to him, and you have no evidence to show that he did the work and charged you for it, then to be honest, I wouldn't bother trying to recover anything in the Court.
If you do have an Invoice/ receipt from him, and he doesn't show at court and tries to ignore the proceedings, then the likelihood is that you will get judgement in your favour.
If you have legal cover on your house insurance, use it to get advice, and representation, if it gets that far.
