Reasonably straightforward (in theory at least)...
Whichever responsible person (RP) manages the various areas in the building has the responsibility to make suitable arrangements for those areas that they manage and control. They have a further duty to co-operate with any other RP who manages the locations that serve those locations (or are served by it). So... one model (but by no means the only one) might be that the Landlord has responsibility within the common parts, but once the mobility impaired occupant is past the front door of the tenancy then the task passes to the tenant. The two have to co-operate to co-ordinate their plans, so both have an obligation to work together to ensure that their management strategies integrate so that in all reasonably foreseeable circumstances there's a workable means of getting any disabled occupants to a place of safety (without placing them at unacceptable risk in case of fire).
There's no need to worry about who would carry the can if things went wrong and the various RPs ended up in court - because the reality is that the Fire Authority will just prosecute everybody & let the courts decide who's in the wrong!