1. Assuming the water comes from a vented hot water cylinder which is itself fed by a cold water storage cistern, then it can be done. You would need a single impeller pump.
2. There are two main types, positive head and negative head / universal.
2a. If the pump will be fitted at the level of the base of the hot water cylinder, and there is a drop of around 600 mm between the base of the cold water storage cistern and the highest hot outlet (usually the shower head) you can probably get away with a positive head pump.
2b. If the conditions in 2a are not satisfied you would probably need a negative head pump.
3. It is not just a simple as buying a pump and connecting water and electricity. It needs to be planned, and a sketch of the various cisterns, cylinders and outlets with relative heights is very useful.
4. Don't forget it will need an electrical supply.
5. They are relatively noisy, and will of course run every time you turn on a hot tap or shower. Can be a nuisance at night.
6. If you decide to go ahead, I would recommend the Stuart Turner brass bodied "Monsoon" range. Well made, long lasting and you can get spares for them.
7. When you decide on the make and model you want, study the installation instructions which should be available on-line. Make sure the pump will do what you want allowing for water system component placements.