shower flow rate

[nameallreadytaken]

just fitted thermostatic mixer tap with shower attachment but flow rate is too slow to hold open shower divert. cold water is mains fed, hot is gravity fed(bath also slow to fill at 38C) could i cure problem by fitting single impeller pump to hot feed? would 1.2 bar be enough? where should pump be sited in pipework(just bath/shower or beside tank for whole house)?

 

[hi-spec plumbing heating]

what is the make and model of the taps ?
as most thermostatics have to be balanced pressures

 

[nameallreadytaken]

make and model not given(ebay purchase) no markings on box no instructions