The feed is shared with at least some of the other flats, but I doubt
if that will cause any problems as the tank and supply are both
substantial - the downpipe is at least 60mm where my private 22mm
branch comes off!

It'll probably work then. Turn the pump right down so you don't reduce the
pressure in the shared downpipe.

You may still get issues, though. Firstly, your lease may explicitly forbid
it. Secondly, the transmitted noise through the pipes may be considered a
nuisance.

You should certainly get a top quality pump designed to reduce vibration and
use it on a low setting.

Another alternative which will always work, if you're lucky enough to have
the space, is to simply have your own tank fed from the communal one and
pump from there.

Christian.