I can't see the image you posted, but it is irrelevant as I doubt if any shower that uses the bath taps will work better than the mixer you already have.
The reason is the height of the header tank. For the shower to work satisfactorily, the shower head has to have enough pressure (head). Generally this means the head must be at least 1 metre below the base of the cold water header tank. My guess is your tank is sitting on the joists in the loft or worse, in the airing cupboard??
The only way to solve the problem is to raise the height of the tank, fit a booster pump or (the most common in rental properties) fit an electric shower that uses only the mains cold.
If your taps are dribbling then it would be a cartridge issue in which case get onto the manufacturer for a spare part and if possible get some ceramic cartridges as these really stop any leaks or drips and are just a couple of quid.
"If your taps are dribbling then it would be a cartridge issue in which case get onto the manufacturer for a spare part and if possible get some ceramic cartridges as these really stop any leaks or drips and are just a couple of quid."
No Mike its not the tap which is dribbling its the shower because the OP doesn't have enough static head to get a decent flow rate. Plumbob has given the correct answer.
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