Cracked floor tiles over pipes

[jbd]

My15 yr old bathroom has 5 tiles cracked in two lines over the feed pipes to a radiator and the washbasin. I believe they are probably laid direct onto flooring board given that the en-suite which has had to be refurb'ed for other reasons was. I don't want to strip out the whole room on cost grounds so would like to replace the floor only (the only joins between floor and wall tiling are behind toilet enclosure and I have a few spares).
1. Presumably it would be stupid to lay new tiles over the old?
2. What is the best solution to provide proper insulation for piping/tiles and as a bed for new tiles? I probably have an additional 10-12mm depth to play with. Is 6mm Hardiebacker Board the best and will it give enough thermal insulation to stop the problem?
3. Are there any types of new tiles to avoid in this situation?

 

[foxhole]

Hardibacker should be ok, if they were laid on floorboards the heat would have dried the cement and small movements in the boards would have cracked them.Problem is not down to the type of floor tile, unless of course they did not use floor tiles.