@morepathsplease, if I may throw my tuppence in here; I manage the account for our communal stair, having ditched our ridiculously expensive factor many years ago in favour of self factoring. I can offer a few observations and more advice if you need:
1) Account is a Treasurer's Account with RBS, although most banks offer similar, and is named 'Residents of <stair number / street>'. The account is not interest paying, but does not charge for any services so works out well for us.
2) Every dwelling on the stair pays £100 twice a year, (9 flats) which covers fortnightly cleaning and monthly gardening (we have garden front and back), as well as a small amount leftover to the communal emergency fund. This is WAY cheaper than a factor would charge.
3) Make sure you get as solid agreement to basic rules from all dwellings. For example: what happens if an owner leaves and wants a share of the surplus in the account? What are the formal collection procedures if an owner does not pay either the regular payment or to replenish emergency funds? What will the maximum carry balance of emergency funds be? Who will be the final and binding arbiter in the event of a dispute?
4) Agree a 'Stair Manager' and an Auditor who will preferably rotate amongst owners every few years. As long as all accounts are audited (which really only involves cross checking expenses against the bank accounts) everyone should be happy.
5) Pay everything (cleaning / garden etc) by standing order. It will make audit SO much easier.
That should get you started, but feel free to ask if you need any more!