We have a large room that we want to use as a bedroom and it has been tiled, over a concrete slab. On further inspection we now realise that there is a slope of approximately 5cm from one end of the room to the other. There are no cracks in the tiles, and I don't want to pull them up, if I can help it. I would like to put something like timber laminate over the top, but need to level the floor first. What can I use that will adhere to the tiles and enable me to fix laminate, or floating floor, over the top.
There's actually no need to level the subfloor to install a hardwood or laminate floor. The subfloor needs to be flat, not level. Now, leveling out the floor may have other benefits, of course. But, strictly speaking, it isn't necessary for the type of flooring you want to install.
There is no reason your tile is any worse of a binding agent than concrete. As long as you clean and etch tile then hit it with the specified primer you should be good to go. Doesn't hurt to call manufacturer or check their website but I don't see anything wrong with this at all. You would have to use some sort of floating floor over this.
Self-levelling underlayment (or floor leveling compound) - basically runny, usually gypsum - based cement product. Read the label before buying - get one that can manage the depth you need, or figure out how many layers you'll need to pour it in - some can be poured full-depth, others may need to be 1/2 inch or 1 cm at a time.
One example (image from US Gypsum, the maker) - there are MANY brands and variants.
There should be no need to etch the tile. Nothing is going to be applying "peeling" forces to the interface, so the leveling compound sits there on the tile which sits there on the concrete - it's going to stay put until the concrete slab fails, if that ever happens. This type of material is often successfully used over much less ideal substrates.