That's something I never understood. The British Police don't carry guns (at least I don't think they do) ...
Cultures and responses are necessarily different. The UK is hardly known as a land indifferent to law and order. I'm no expert, so take my response FWIW; but a couple of things come to mind. Kindly correct me if I'm off-base.
First, I believe the UK fuzz have adapted to the brave new bang-bang world with a layered response to the threat. Many have training and access to firearms, but do not carry them into every situation unless there is reasonable apprehension that they may be needed. This is a reasonable compromise to the traditional role, in their view; and no doubt there are very heavily armed responders who deal with additional escalation. (Keep in mind that the UK has dealt with very real threats, internal and external, for an extended period.)
The second thing is perhaps understood (traditional) rather than codified. At least that's how I read it. A "firearms last resort" policy implies a "hands-on physical control first" policy, with perhaps a great deal more lattitude in how physical force is applied.
Anyway, that's my 2p.
As an afterthought: in these discussions, you have to read through the usual Brit understatement. E.g., a full-bore, two-fisted interrogation comes out as "the gentleman is assisting the police in their enquiries."