Judging by some of the posts on this thread -
What is Freesat? - if there's already a communal Sky dish, it should also be OK for BBC/ITV Freesat reception . As regards having a new communal dish installed, this may not be straightforward, as you'll not only have to get the agreement of the landlord, but also of other residents (unless you're thinking of paying for it all yourself). Planning permission from the local Council may also be required.
There may be a further snag concerning the Freesat equivalent to Sky+. Apparently, Sky+ requires
two connections from the satellite dish, and few
communal systems seem to allow for this. If Freesat recorders are of a similar format, then a communal dish may not be very useful, and you may have to think of installing your own dish - or of course sticking with a Freeview OVR which doesn't require two connections from the aerial.