OK.
As I suspected, the cold water comes at high pressure from the watermain, and the hot at low pressure from the loft tank. You cannot get a satisfactory blend from an ordinary mixer.
If you have any ceramic mixers with a single lever or joystick, they may get worn and develop internal leaks causing the cold tank to overflow. Mixers with two knobs or capstans will be ok.
You can have a pumped shower, but it must draw the cold water from your loft tank. The loft tank must he big enough for your bath or shower without running dry.
Start by asking around for a well-recommended and experienced local plumber. As soon as possible, and before s/he comes, use a green nylon washing up scourer to clean all those green and scaly marks off the pipes. If they come back, the joints are still leaking.
The pipework is quite whimsical. The plumber will need to see it all, but afterwards, use Climaflex or similar stiff plastic foam pipe lagging to reduce energy wastage.
Also, send your photo, with any identification on the labels, to Gledhill and ask them what model it is. Also ask if they have an approved local installer/repairman in case it needs skilled attention in future.