I assume that you have a private landlord....
If the heating was in situ and there's isn't a clause within your tenancy agreement that specifies that the tenant is responsible for the maintenance, repair and/or replacement of the heating. Then the responsibility is the landlords.
So what can be done...
If you have given the correct notification to the landlord, and the landlord is either refusing or has failed to arrange for maintenance, repair etc, after a set period the tenant can legally arrange for maintenance repair etc and have the contractor send the bill to the landlord for payment. There is a set procedure though, so it's is wise either to contact your local citizen Advice or local council housing office, so they can check that you have the right and have followed correct procedure before going ahead.
As to disabilities and entitlements
When it comes to heating side of home.
The law say's that people who have children under 5 or are themselves elderly (above pension age) can't not have water or fuel cut off...
But most organisations do have an 'Vulnerable Persons' register which you would need to fit the organisation criteria (can be different for each organisation) this can entitle the individual to priority, concession or protection dependent on organisation though
In the case of council or housing association, it will give you an higher priority for an repair both in it's deemed emergency, and the timescale that the repair needs to be carried out.
Heating wise, there's no particular legislation that heating or it's provision is required to ensure a min temperature etc... However there is an EU directive that effects social housing where heating is being provided.... It based on fuel poverty...
Where equipment is provided for heating, then the running cost most not exceed an set percentage of the income, if it does and the equipment is old and outdated, then you can enforce replacement to a new more efficient heating equipment.
