Hot water from bath taps but cold to luke warm from shower head above

Presumably, the shower has worked fine until recently? If so, you may already have some sort of valve installed to balance the water pressures on the inlet side to the mixer taps - either a pressure equalisation valve or a simple none-return valve on the hot side. This valve may have failed, or if you've had work carried out recently, it's been known that the cold pressure has been reduced by a previous 'plumber' by simply partly shutting off the cold water main stop tap. If you have had work done recently, the stop tap may have been returned to fully open, causing this problem. If it's something that's been going on for a while (especially since installation), then it almost certainly is a case of the hot supply to the mixer being tank/cylinder fed and the cold being mains fed. Ideally, removing the cold feed and replacing it with a feed from the same cold tank as where the hot cylinder is fed from (ensuring equal hot and cold pressures and flow rates being delivered to the shower) with a plus point of being able to install a twin impeller pump in line with the mixer to drastically increase the pressure to the mixer shower. If you do go down the twin impeller pump route though, make sure you install either a Surrey or Essex flange to the hot water cylinder to ensure an air-free supply to the inlet of the pump - failing to do this will invalidate any pump warranty in most cases. Best of luck Dave - DrainMedic

Sounds like unbalanced feeds to the tap, the cold high pressure over rides the hot and forces the hot water back through the system, you need a pressure equalization valve £47.00 from BES plumbing supplies, based in Birmingham, http://www.plumbingsuppliesandfittings.co.uk/Water_pressure_equalising_valve--product--80.html