The 1985 Act says in its section 11(1)(c):
There is implied a covenant by the lessor to keep in repair and proper working order the installations in the dwelling-house for space heating and heating water.
This applies to many but not all residential leases, and is effectively an extra clause in the tenancy agreement. It does not say in detail what is meant by "keeping in repair". The courts have recognized situational differences between properties, for the type of heating system, how broken it is, the time of year, who the tenant is (e.g. if they have young children), and what alternatives they have while the repairs are awaited. They can and do award damages, but don't often order "specific performance" (telling the landlord exactly how to proceed), because there may often be several available options about how best to make a repair or upgrade. As an example, landlords may provide inefficient space heaters as a stopgap, but tenants who pay the electricity bill might not want to use them. Heating may work in one room but not another: is it convenient for the tenant to change where they sleep?
So this particular law does not force landlords to act in a timely fashion, as there are so many situational oddities where a court is better-placed to figure out what is reasonable, rather than the legislature setting the parameters in advance. What does happen in terms of damages is that the court will look at the interval between when the landlord found out about the problem, and when they fixed it. (And under the Defective Premises Act 1972, section 4, the landlord has a duty of care which can start the clock at when they ought to have known, rather than when they did know.) If that period is many months, then the damages, being assessed as a proportion of rent, will be larger - and the chosen proportion will depend on all the circumstances at hand, including the attitude of the landlord. The proportion can exceed 100% if the circumstances are particularly bad.
That said, there are many other provisions of housing law which can apply to set a timetable. Under the Housing Act 2004, there is a complex regime which can lead a local council to issue an "improvement notice" to the landlord, in case of a hazard to health. They can also give a "prohibition order" which stops people from living on the premises and triggers the provision of alternative accommodation; and even intervene themselves in an urgent situation, effecting a repair instead of the landlord.
The regulations under that Act specify a scoring system (the Housing Health and Safety Rating System, HHSRS) for assessing hazards to health, based on many factors. I won't go into the numeric details. One of the possible outcomes is a finding of an "excess cold" hazard, which is scored with reference to a hypothetical 65+ year old person living on the premises. You might like to read the CIEH Enforcement Guidelines which detail some of the technology and statistics behind the scoring system, and considerations for remediation.
For an ordinary improvement notice, the landlord has at least 28 days before they are required to actually do anything (section 13(3)). That is shorter under the urgent procedure, but that can only be followed if there's a "category 1 hazard", plus an "imminent risk of serious harm" to the occupiers. This requires the loss of heating to be an actual threat to their health. (But it may coincide with other safety grounds, such as food safety when there's a loss of electricity, water damage from leaking pipes, etc.)
In Bolton Metropolitan Borough Council v Patel [2010] UKUT 334, emergency repairs were made by Bolton MBC on three grounds: excess cold, food safety, and electrical safety. This happened the day after the council's inspection of the premises. The landlord took the case to the Upper Tribunal, which upheld the decision of the tribunal below that the council was justified in making the repairs, but also found that the "imminent risk" threshold was not met in the case of excess cold. The council had assessed that by looking at a five-day forecast which indicated that the weather would be cold. The tribunal said that it was, however, not unusually cold for the time of year (November!), and that since the occupiers had already been without central heating for several months, the risk was not imminent. They had access to halogen heaters, which didn't work very well, but were also not nothing. That's one case, albeit in a court of record, but it's indicative of what might get treated as an emergency requiring immediate action.
For tenants in local authority housing, other regulations do give a tariff:
Total or partial loss of space or water heating between 31st October and 1st May - 1 working day
Total or partial loss of space or water heating between 30th April and 1st November - 3 working days
Exceeding these bounds causes compensation to be due to the tenant, but that is capped at fifty pounds.
The safety arguments under the Housing Act 2004 can also be alleged under other legal cover, such as the Environmental Protection Act 1990, section 79(1)(a), by which a local authority can intervene in "any premises in such a state as to be prejudicial to health". It's an offence to disregard the resulting "abatement notice", with the penalty eventually reaching £500 a day if the landlord does not comply. (That's not payable to the tenant, but it ought to be something of an incentive.)
