Short answer: usually yes. Renting doesn't take you out of the picture — it just changes which parts of the building are your responsibility versus your landlord's.
Who counts as the “Responsible Person”
UK fire safety law puts the duty on whoever has control of the premises day to day, known as the “Responsible Person.” In a rented unit, that's usually you, the business running day-to-day operations, not the building's owner. It doesn't matter how small the business is or how short the lease — if you're operating from the space, the duty to assess and manage fire risk generally sits with you for the areas under your control.
What's on you versus what's on your landlord
Where it gets split is shared infrastructure. If you're a single tenant in a self-contained unit, you're typically responsible for the whole premises. If you're in a shared building — an office floor, a unit in a parade of shops, a space inside a larger complex — your landlord or managing agent usually holds responsibility for communal areas: shared stairwells, fire doors in common parts, the building's central alarm system. You're generally responsible for what happens inside your own demise: your fire extinguishers, your internal escape routes, your own fire risk assessment for the space you occupy.
What to actually check in your lease
Most commercial leases have a clause addressing fire safety responsibilities, though the wording varies a lot. Worth specifically looking for who's named as responsible for the fire alarm system, who maintains shared fire doors and escape routes, and whether there's a building-wide fire risk assessment your landlord already holds (and whether you've actually seen a copy). If none of that's clear, it's worth a direct conversation with your landlord rather than assuming either way.
What happens if it's genuinely unclear
In mixed-occupancy buildings, the law expects everyone with a stake in the premises — tenants, landlords, managing agents — to cooperate and coordinate on fire safety rather than each assuming someone else has it covered. If you're unsure where the line sits, that's a reasonable starting point for a conversation, and it's exactly the kind of thing a proper fire risk assessment will clarify rather than leave to guesswork.