Fink - Yes the vast majority of UK police do not carry guns or even tasers.
Having said that nobody in a large town or city is far from specially trained mobile armed officers. Since the Manchester attack they have been highly visible on the streets. I was in Newcastle last week and counted 6 officers with automatic weapons in a small area. In london a large number of armed police are out in force in vehicles all the time. I believe they also had helicopter support.
Most Brits approve of keeping a mostly unarmed force. A policeman with a weapon has to interact very differently with the public in order to protect his own weapon. With unarmed police an aggressive drunk is likely to get taken down by a few officers working together very professionally to protect themselves and the idiot they are arresting. Everybody goes home to their families. As we see all to often in the USA potentially minor incidents can escalate quickly with fatal consequences.
I don't believe all police have the suitable psychological skills to be armed. In the UK police have to pass rigorous selection and training to be armed. The course has a high failure rate.
Most UK officers will never encounter a criminal with a gun during their career.