If you paid for the slate to be laid I'd be tempted to get the person back to do it for you.

Did you make it absolutly clear to the guy laying the slate you wanted a level finish? If so then get him back to do the work for you....I can forsee the whole area of slate having to be taken up, the ground levelled and the slate put back. A long back-breaking job.

Don't touch a thing!!! Take pictures of this job at many different angles. Make a full written description of what you see and what your concerns are and how this upsets you. Next get a written estimate of how much it would cost to fix the problem. Now, I am from the USA so what I am going to tell you , you will have to take a comparable remedy from the UK perspective. I would go to small claims court an file a lawsuit for the amount that I paid this person plus the amount it would take to correct the situation plus court costs. I would not need a lawyer at all. The court clerk would give me the necessary forms to fill out and I would attach all records required: photos, written description of damaged done, receipts estimates, etc. The court clerk will register my suit and set a court date. The clerk will then give me law suit papers which I would have to present to the person I am suing, the court does not do this. I can serve the papers either by registered mail return receipt requested or for a small fee the county sheriff can serve him personally. One important thing, I Must Spell The Name Of This Person Correctly!!!
Then I arrive at court at the appointed date and time. If the person I filed the complaint against shows, the small claims court judge will settle things. If my adversary is a no show in court, judgement will be made against him and then a lein on his pay or property can be place upon him. Again, I strongly advise you not to attempt to correct this botched job, if you do,you will have lost your remedy available in court if such is available in the UK. Small claims courts in the USA handle cases involvIng recovery of damages from $1,500 to $10,000 depending in which state it is filed. Why would you have this person back? If he did not do things right the first time he sure as heck doesn't know how to do it right the second time!