That would be amazing if they could. I am based in Luton, Bedfordshire. I'd be happy to pay someone to come out and give me their professional opinion.
Like I said, I would much rather a professional tiler redo the work. I plan on calling this guy, telling him my findings, and see what he says (although I can guarantee he will try and fob me off). I will then politely inform him to expect a letter from myself. In the letter, I will state my findings, with the required literature, and then specify a date in which I wish the work to be complete. I intend to include a quote from someone else, and if they cannot complete the work in the time specified, then they will be billed for the cost of redoing by this other professional (this is all inline with Consumer Rights - the process to follow as defined by them).
The company was actually based in luton, but they moved up north (a good few hours drive away). I also know that he is apparently fully booked for the next several months.
So in conclusion, if anyone else, local to me (bedfordshire Hertfordshire) is happy to come and look, there could be an additional job in it for them. Preferably to be complete before Crimbo!