Pump required to increase cold and hot water pressure

Have domestic gravity-based system with hot water tank for central heating and general water use, and need to know any recommendations for the type of pump to increase both hot and cold water pressures, and the strength of pressure required.
Have two bathrooms.
Cold water tank is in the loft.

You need a minimum 2 bar pump; Stuart Turner Monsoon standard S2.0 or Salamander RHP 75 2.25 bar for positive head system. If negative head is require - ST Universal U2.0 or Salamander ESP 75 2.0 bar. Location of pump, any up & over pipe work & shower heads will dictate if you require + or - head. The pump & pipe work must be correctly installed with suitable HWC flange to avoid problems & possible damage to the pump. They will use a lot of water very quickly so you need to ensure you have adequately sized hot & cold water storage tanks.

Excuse my ignorance but although you mention that both cold and hot water will be used very quickly, isn't the rate of flow dictated by the taps or shower controls/tap.?
Many thanks.

Yes but if you stick a 2 bar pump on the supplies you could be chucking out anything up to 15 litres/a minute per shower/tap on a 22mm piped system. It depends on what showers/taps you have but even a basic pumped shower will deliver at least 8 litres/min & if you have a drencher head fitted, it will be much more. The cws tank also feeds the hws tank & if your running H&C together, the incoming mains won’t keep up with that & if you run 2 showers/baths simultaneously, it gets even worse. The cws tank will empty quicker than the mains can fill it & sometimes a cut of float switch has to be fitted in the tank to turn the pump off when the water goes below a safe level.

The minimum size cws capacity you should have is 250 litres & to avoid running out of hot water half way through your shower, 150 litres is the minimum & even that will only last 10 minutes at maximum flow before it starts to go cold on you.