I've been to the UK a number of times in recent years. The idea that UK cops, and particularly London cops, go unarmed is unalloyed bullkitten. The difference is that they jump directly from baton-and-spray to MP5-class sub guns with 3 spare mags. While I grant that my last trip over there was immediately before the start of the Summer Olympics, so security posture was a bit stepped up from usual, I didn't go a single day without seeing London cops on foot patrol with MP5s. This was consistent with my previous visits, FWIW, especially around transit stations such as train terminals and airports.
Get out of the major cities, though, and the polarity flips back to the stereotype of "unarmed constables except in dire emergency".