Does Awaab's Law apply to me?

For this tenancy

The duty still applies, without a fixed deadline

the statutory response periods are social housing law, so they do not reach a private tenancy, but the duties below do

• WhyThe periods come from regulations made under section 10A of the Landlord and Tenant Act 1985, and section 10A(6) reaches a lease only where the landlord is a registered provider of social housing and the home is social housing. Section 60 of the Renters' Rights Act 2025 would extend an equivalent regime to private tenancies. It is not in force.
• What does applySection 11 of the Landlord and Tenant Act 1985 puts the repair of the structure, the exterior and the installations on the landlord. The duty arises once the landlord is on notice and the work has to be done within a reasonable time. There is no fixed number of days, and reasonable is measured against the hazard.
• The other dutyUnder the Homes (Fitness for Human Habitation) Act 2018 the home has to be fit to live in at the start of the tenancy and throughout it. Damp and mould is one of the matters that goes to fitness, and a tenant can bring a claim directly.
• Who enforces itThe council's environmental health team, under the Housing Health and Safety Rating System. They can inspect, score the hazard and serve an improvement notice. A tenant does not need the landlord's agreement to ask them to look.

Dates still decide these cases, because the duty runs from the date the landlord was put on notice. Keep the report as it was made, keep the date the landlord became aware, and keep what was done after it.