I am not going to suggest to fit old blanket or dust sheet behind as Others on this forum who has a lack of tiling knowledge I am affraid.
The cheapes and quicker option could be shower splashback fitted on to existing tiles which if is fitted properly will last for ages.
I have fitted showerwall systems and they were brillinat.
Showerwall is the ultimate versatile easy to fit waterproof panelling system, with a moisture resistant MDF core and high-pressure laminate backing that's designed to deliver a smooth, watertight finish that's tough, hard-wearing, stain resistant and totally hygienic.
This can help
My advise is to remove the existing tiles and replace them, if you tile over them it could cost you twice as much in the long run, check the wall behind is sound and firm, seal the wall with PVA glue and water to form a good surface for the adhesive to adder to especially if the wall behind is painted.
Bespoke contractors LTD
Best would be to remove existing tiles and get new ones. Would be wise to spend around £10 to £15 for proper bath & shower protection (polythene backed heavy duty dust sheet) and if you have any old blankets - they might come handy as well. All depends on condition of walls (brickwork or plasterboard) - it can be the case you will have to rebuild it quickly before new tiles.