Bath Mixer tap with shower problem????

[Cometomama]

HI and
Merry Xmas to you all.

My electric shower have busted again so this time I have bought a Bath mixer tap with shower instead and replaced it with the two taps.

Cold water is coming from Tank (just above the bathroom upstair) and hot water is from downstairs Boiler (BAXI 105e).

the cold water pressure is not good as hot water and when the shower is on the hot water takes over and only hot water is coming out of shower.even I put the cold water on FULL and hot water just a bit it still impossible to have shower.
And If I close the hot water altogather there is still hot water coming out of cold water for about 15 secounds from cold tap.

I guess the cold water pressure is not good enough and hot water even pushes it backall the way to the TANK.

What shall I do???
do I have to buy pump for cold water supply from tank??

Is there any way around?

Thanks

 

[keego]

Put everything onto mains, connect the cold main at the tank to the outlet to supply your taps & poss toilet.