The floor tiles in my bathroom are blue and I want them to be white. Is there a super secret product that will help me achieve this, or is the only sensible option to re-tile the lot?
None of the tile paints are recommended for floor tiles. It is relatively easy to tile over the top of the existing tiles (if they are sound and not drummy).
I just did a reno on a bathroom with blue floor tiles, initially thought the same as you, then realised how easy everything shows up on white, pain in the butt, decided to leave them as is. The wall tiles were white with some 80's pattern on them so I painted them white, along with the walls/ceiling, with the vanity & bath white once everything else is it needs the blue floor.
We have done the White Knight tile paint on a floor (although not recommended) and didn't have an issue. Bearing in mind this was an ensuite, so not heavily trafficked. Give them a good clean, use the primer, let it dry/cure properly, then two coats of top coat, again with sufficient time between coats.
I have painted over tiles on two reno's now. Both were wall tiles, the first I treated the tiles with a product called ESP and then used an acrylic paint. The second was a new product which had the bonding agent mixed in and was able to be painted straight on the tiles. Both lasted about 1 - 1.5 years before the paint started peeling in the shower. I would never use it on floor tiles unless it was for a quick fix and I planned to re-tile within a year.