How to fill up bath quicker?

A rented place we are renting at the moment is perfect bar one problem that the whole family loves baths and prefer them to showers, however it is taking absolutely ages to fill up the bath with cold and hot water - pressure seems very poor.

Here is the setup:

Its a 2 storey house, Header tank is up in the loft (also in the loft is a big round black thing with a pipe going into it - I am presuming it might be an expansion type thing for the immersion cylinder), the hot water cylinder is indirect (electric & boiler) in the bathroom on the floor (ie same level as the bath and is not higher than the bath), the taps on the bath are mixer with shower head and a diverter lever to direct water to shower head or bath spout.

Is there any kind of electric pumps (and if so what make/model) I can fit from the pipe out of the bottom of the header tank (for increasing pressure for the cold water for the bath) and a electric pump i can fit from the top exit of the hot water cylinder for increasing pressure for the hot water for the bath) because just gravity alone doesnt seem to be enough pressure (well not upstairs at least on the ground floor in the kitchen and downstairs loo the pressure is really good - more gravity I suppose). Can a central heating pump be used (those grundfoss with the 3 speeds on normally used for radiators) to increase the pressure coming from the header tank?

Any Ideas please - many thanks.