I have put new work surfaces on, so turned water off. When turning water back on, the cold came out but no water through the hot water tap. I have tried a pipe from one tile to another, but no joy

Hi Gary and welcome, sounds like you have some debris in the system, here I would turn off water, remove the hot water cartridge and try to flush if you get good pressure there you should be good to go, if not move down to the supply line and take apart and flush, keep going until you find the blockage. Be sure and check the shut-off valve as the problem could be there. An expert should be along with more help so check back and let us know how it goes. Good luck