Quick answers
Can new tiles go on top of the old ones?
Sometimes, if the old ones are firmly stuck and flat. But the old pipes stay hidden underneath, and if some tiles are loose or sound hollow, they all have to come off.
Laying tiles over tiles sounds quicker and cleaner than a strip-out. In some cases it can be done: when the old tiles are firmly stuck, flat and free of cracks, and their surface is prepared so the new tile adhesive can grip.
But a new tile is only as sound as the old one underneath. If some old tiles sound hollow when you tap them, or have already started to fall, they will take the new ones with them. In this bathroom, the dark old tiles had started to come loose on their own, so the only proper answer was to take them all out.

There are other limits too. With one layer on top of another, the floor gets higher, and the door, the drain or the threshold may need adjusting. The old pipes stay inside the walls, and you can't move the fixtures or build a walk-in shower, which needs a new floor laid with a slope.
In the bathroom with the green bathtub, the tiles, the tub and the old render came out down to the brick so the pipes could be replaced as well. If a bathroom only needs freshening up, sometimes the tiles can stay and the walls above them are repaired.
Whether your tiles can stay as a base is decided on site, by tapping them one by one and looking for leaks and damp.
Jobs that show it

Bathroom Renovation with a Walk-In Shower
A bathroom with dark old tiles and a tub was stripped out completely and became a bright room with a step-free shower, a wall-hung toilet and a new basin.
See the job step by step

Full Bathroom Renovation: From a Green Bathtub to a Walk-in Shower
A bathroom with old tiles and a green bathtub was taken back to bare brick and rebuilt from scratch: pipework, render, tiles and fixtures.
See the job step by step

Bathroom With Peeling Walls Restored
The walls and ceiling above the tiles were stained by damp and peeling. The old fittings came out, and the surfaces were repaired and painted white.
See the job step by step