Okay first, you have my sincere sympathy for that job.
I'm no legal brain and do not, honestly, know where you stand regarding a claim, or the steps and timeframe involved, so I will not pass any advise in relation to that.
I do know, however, that the tile job you have received is absolutely shocking and way below the standard of anyone that would expect payment for said work. It is difficult to criticise a job when you only have a few limited pics, so my advise would be to request that a local tiler visit and provide a full report on the work. The report will not only focus on the aesthetic aspects of the job, but more importantly, on the safety aspects. Even if you have to pay £50 for the report, I'm confident that you will have sufficient information to seek legal compensation and a job completed correctly.