It depends what you mean by communism or socialism. Your tone implies your definition includes authoritarianism, which it doesn't have to.
Fundamentally, socialism is just the principle of taking stuff from everyone, centralizing it, and using the funds for collective good. Ie: health, or roads, or armed forces.
In other words, the UK already is, to some extent, a socialist democracy.
The question is then, how far down the socialist route would we want to go. Some people would like there to be less socialism (lower tax, more individual responsibility), some would like more socialism.
There are very few people who want no socialism at all (full libertarians like Elon Musk) in the UK. And also very few who want full communism like China of old. And vanishingly few either side of the debate who want authoritarian rule.