It's a big mistake to think that the British police are unarmed. They're not.
They just don't bother with piddling little pistols.
If you're going to have a gun, have a BIG GUN.
Other than for plain-clothed detectives working undercover, pistols are pretty much laughed at by the British police. Compare the stopping power of a weeny little Colt or a Glock to that of an MP5 sub-machine gun, G36 assault rifle or (God help you if you see one of these - strongly suggest you change your plans for that day) an SA-80 or AR-15 assault rifle.
Although British police don't routinely carry sidearms, in high crime urban areas they will carry SMGs or assault rifles in a locked gun cabinet in the boot (trunk) of their car. In extremely difficult or vulnerable areas such as airports or tourist hotspots, they will carry MP5s around, mixing in with the crowd. The bobbies carrying MP5s are very nice blokes, feel free to strike up a conversation with them. Just back off the ones carrying SA-80s and AR-15s, there's a good chap.
Our largest island is only 700 miles long. Where on earth are you going to run to, that a radioed-ahead armed response unit can't get to first?
I can fully understand why lots of larger countries have routinely armed police - calling for backup could take hours. But it's extremely difficult to outrun the police radio on an island only 700 miles long with a heavily-armed SMG & assault rifle unit every 25 miles or so, and CCTV at every trunk road junction (interstate intersection).
(The police at Birmingham Airport used to have those truly lovely-looking P90 bullpup rifles for manoeuvrability in corridors & aeroplanes; from my recent visit it looks like they've swapped over to MP5s - a shame as the bullpups just looked like a wonderfully practical bit of design. I once saw West Midlands Police using one of those wacky Steyr Augs - again, lovely design - but seem to have standardised now on SA-80s and AR-15s. There seems to be a lot more standardisation across the various regional firearms units these days. Probably very practical from a co-ordinated response point of view, but a lot less showy from a nerd point of view.)