Rubbish hot water supply

I've just bought a 1 bedroom flat, 2nd floor and the current water system is cold water tank with hot water cylinder below. The shower is a Mira electric job (not the best). The mains pressure seems fairly strong (kitchen tap powerful), although I've no reading of the actual pressure. My problem is that the hot water taps run at very low pressure, the kitchen (furthest from the cylinder) practically does not run. Its through a mixer tap and when cold is added, the hot seems to be overcome and disappear.
I am struggling to decide what to do, my initial plan is to get rid of the tank and cylinder and fit an electric combi (no gas available). This would give me more room in the cupboard. From research I have realised that a mains pressure hot cylinder also may do the job. I would also like to incorporate a powerful shower into the system if possible. The cupboard, kitchen and bathroom are all next to each other so no long or complicated pipe runs are required.
If all this is going to be too expensive I may change the shower for a built in mixer and add a pump to up the pressure to this and the hot taps.
Any advice on the best course of action would be greatly appreciated,

Cheers
Stewart

Cheapest option is to add a pump about £200-£300.

Best option is an unvented cylinder about £500-£1000 needs good mains FLOW and certified installer.

Tony

Cheers,

Im going to go for an unvented direct cylinder as there is no wet heating system in the property. (Heatrae Sadia or similar), will this and a cold feed from the mains be adequate for a powerful shower? Otherwise I'm looking at a cold tank and pump setup. Is it OK to feed a pump from an uv direct cylinder? and will a mains feed struggle to feed a tank and cylinder simultaneously whilst the shower is running?

maybe the taps are mains pressure taps.therefore not suitable for gravity hot water.