Can the pump on a pumped accumulator tank be installed separately from the base of the accumulator tank?

Yes, the pump can be installed remotely from the vessel.

It must be installed within 5 meters of measured 22mm pipework (this can include a maximum of 2m of 15mm pipe) of the point of entry for the mains water into the property, usually the same location as the stop-tap, and must be the first thing in the system.