How do you find the person address by mobile number in UK?

There is no perfect way to find one but these are the methods one could try out.

Internet Research - Using search engines or social networks with public profiles and type in the number to get clues from the results.

Free people search engines - These include sites like Wink, Jigsaw, Zoominfo and similar.

Reverse phone lookup - These can be both free and paid ones.

You typically can not without a court ordered warrant. The area code can give you a general area and reverse searches such as www.zabasearch.com can give you a name to then search.