Tell them you can set the test up and they can come and witness it. I would not want to spend £400 just because someone is being a numpty. Part of what you pay for is inspections.
DON'T PAY ANY MORE! Write to them explaining that the work is not satisfactory and you will be withholding all further payments. Attach the photos. Reserve the right to claim all expense to rectify.
The work is so bad that I would not offer them the chance to return and make good. Your new firm will need to strip the whole thing and start again. Make sure you see some completed jobs and have a chat to customers.
You may as well get someone to supply and fit, as you need to meet electrical and Fgas regs. They are probably busy now. Have a ring round in a week or two.
These are often standard drawer boxes from Blum etc. Have you ended up with things that don't fit? Did the supplier have a showroom or any information on the drawer depths?
A friend was doing and agricultural shed and he went for timber frame 8 x 2s as you only need to nudge blockwork with a telehandler and it collapses whereas timber frame bounces back if it is constructed correctly.
The 22mm is annoying but is only 1mm per metre.
With the sub structure stuff it will be possible to rectify but I would point out that I expect it built as per drawings. Better to let him know as he progresses than after he has finished. Check the drawings each day and go through with him in the morning where you think he might mess up.