Vinyl/cushion flooring over ceramic tiles

The tiles should really come up, then screed the floor with self levelling screed but this does leave a height difference between floor and skirting so that would need adjusting, then re-painting etc.. If you want to screed over the tiles, it's essential they are all firmly fixed down, wash with degreasant/detergent, let dry, prime the tiles (most bags of screed will recommend what to use as a primer) PVA can be used on some, others require a neoprene primer, both quite cheap and easy to use. Then lay the screed. Remember a screed doesn't just lay itself, you need to trowel it carefully !! A pro would also use a spiked roller to pop any bubbles that arise. I've noticed B&Q are selling Mapei primer to go with their self levelling screed and most Mapei is quality gear. A pro could screed your area in an hour, might be worthwhile getting one in !!

The answer given above is pretty accurate, although you never use pva on a subfloor you can't screed over this or it will fail.

The best option is to use one of the newer levelling compounds and primers, made by Uzin or Ardex, specially designed to go over ceramic tiles and get a professional floor layer with knowledge about these things in to do the work for you.