Cold water leaks downstairs when shower used

How do it is cold water? Does leak occur when only cold water is turned on in the shower or does it occur when either cold or hot water is used?

How do it is cold water? Does leak occur when only cold water is turned on in the shower or does it occur when either cold or hot water is used?

When either hot or cold are used, shower has mixer tap not separate taps

You need to first determine where the leak is occurring. Is it coming from the water supply system, from the drain or from the shower pan?

You need a flat rubber drain stopper, a threaded PVC pipe cap to fit the shower arm and a bucket. Here in the US the pipe cap size would be 1/2".

Stop the drain with the rubber stopper. Fill bucket from another source, not the shower. Using the bucket pour enough water in the shower to completely cover the floor about 1". Look for leak. If leak occurs then leak is in shower pan or floor. Highly unlikely. Remove the stopper and let water drain. If leak occurs, the leak is in the drain system or pipes. Most likely where drain attaches to pan.
If no leak then leak must be in water supply pipes.
Remove shower head and screw on pipe cap. Doesn't have screwed on that tight. Hand tight should be sufficient. Turn on water and look for leak. If leak occurs the pull escutcheon around shower arm away from wall and with flashlight (torch) look for leak where shower arm screws int to riser pipe. If no sign of water remove handle and escutcheon of valve and look there for leak.

In US we often have a panel on the other side of the wall where the valve (mixer) is, so you can service the valve. If you have such a panel remove it and look for signs of water there.