Hi Sammie,
I recently had work done in my house by 2 different tilers and each left behind a mess. I just took it that we had to remove it. We got one of the mini skips. I think they are about a tenner to buy in the supermarket, 3 different sizes. They are really handy to use and when you fill them you just ring the company and pay by cred card over the phone (about 70 euro I think) and they pick it up within 4 days. I got 2 of these skips and on both occassions they were picked up the next day. You could be waiting a long time for the tiler to come back and collect them so I would just save yourself a lot of hassle and get one of the mini skips.