Richard, a little more information would be helpful such as types of properties, whether this is a RSL, Council, whether any HMO's etc. The list is potentially (almost) endless. In addition to the usual suspects on the H&S front (HASAWA, MHSWR, CDM, LOLER, Work at Height, COSHH, Manual Handing, PPE, EAW, CAR etc etc - the list is clearly a lot longer) you may, depending on the circumstances also have to consider Building Regs and possibly 'housing' and environmental legislation. The HSE website has the various 'H&S' information freely available, but the other, such as building regs are I believe, chargeable, although your LA Building Control team may be able to advise/point you in the right direction. Alternatively, try and contact and 'buddy up' with someone from a Council or RSL for a couple of days to try and get a bit of direction.

Housing Health and Safety Rating System (HHSRS)?

Not really, no. LA's are a law unto themselves - little or no consistency between authorities (or even inspectors within the same authority).