low pressure system

I have a problem - low cold water pressure to bathroom and low hot water pressure to bathroom and kitchen. The set up is as follows:

1/ Single story flat
2/ Hot water cylinder sitting at floor level (height 1m)
3/ Cold water tank (height 60cm) supplying the cylinder
4/ The bottom of the cold water tank is sitting 50cm above top of hot water cylinder.

Could I remove the cold water tank from the equation and instead:

1/ connect the the mains pressure cold water supply to
a/ the cold feed that goes to the bathroom
and
b/ the hot feed that goes to the hot water cylinder

I assume 1.a. is okay but what would happen to 1.b.? Would a pressure reducing valve be required?

1.b would explode.
Unvented cylinder would give mains pressure, budget maybe 1500 - 2000.
Or use a pump as
here