First up, apologies. I messed up one of my links. (Ignore the "chrome-extension" bit. Apparently that can't be opened.) Should be:
https://researchbriefings.files.parliament.uk/documents/CDP-2019-0102/CDP-2019-0102.pdf
Do the UK police allow it? Again, I haven't walked through every street in the land so I can't provide an empirical study. I've heard stories online of people being harassed in these "Sharia Controlled Zones", especially women. Which is very not cool.
All I know is if I found myself drinking a can of beer, smoking a cigarette and playing music on my headphones while walking down a street in London (totally legal in UK unless it's in a specifically alcohol-free zone which does actually exist) that had a poster on some lamppost saying "Sharia Controlled Zone", and some extremist Islamist nutter came up to me and told me I wasn't allowed to do that, I think I might well them to bog off and leave me alone. Or tell them to fck a donkey in Arabic or something.
If it was a gang of aggressive-looking young men in balaclavas and hoodies with bigger muscles than me, I might be a bit more cautious tbf. In any case, after stubbing out my ciggy and pouring my beer away, I'd possibly still be cheeky enough to politely ask them what their legal authority was for enforcing this policy. (You can come to my funeral later.)
If I called the police (and they actually turned up within 3 hours lol), I'm not sure said nutters would have a leg to stand on. Shariah-controlled streets aren't a thing in UK law. It's just a bunch of weirdos trying to create their own laws and harass and threaten people in a few areas. I'm not gonna be told to stop drinking a beer ffs. I like beer. If you don't like me doing it, eat my shorts. As long as I'm not shitfaced, causing havoc, harassing anyone, pissing in the street or being generally antisocial and breaking laws, it's none of your business.
We can try an experiment. Any volunteers?
Anyway I had a quick look. This is an old Stone Age story, from 2011.
https://www.dailymail.co.uk/news/article-2020382/You-entering-Sharia-law-Britain-As-Islamic-extremists-declare-Sharia-law-zone-London-suburb-worrying-social-moral-implications.html
Daily Mail is an (arguably) very rightwing UK newspaper that is typically anti-immigrant and likes to complain a lot. Interesting to see how much their rhetoric has evolved in the last decade cos this article reads way more measured than their current stuff. Also way less clickbait and ads.