Now this is entirely based on my own experiences, informed also by what I have read online. Other people living in the UK may see things differently. I have lived in several different parts of the UK, but I haven't lived everywhere.
The UK is not like Sweden, where everybody removes their shoes in homes. However, it is also not like Spain, where removing shoes in homes is seen as unusual.
I would say that the majority of people in the UK do not wear shoes in their own homes 90% of the time. They may not have a rule, they may sometimes keep their shoes on, but most of the time they take their shoes off in their own homes. They also generally require their children and friends of their children to remove their shoes. This may not be enforced strictly, but this is still an expectation.
Most households will not ask visitors to remove their shoes. However, more often than not, visitors will remove their shoes or at least offer to remove their shoes. This often leads to absurd conversations like this:
Guest: Shall I take my shoes off?
Host: You really don't have to.
(Guest notices shoes by the door)
Guest: I probably ought to.
Host: No, you can keep them on. It's really not a problem.
Guest: I'll take them off anyway.
Host: Thanks, that's nice of you. (It's what she wanted anyway)
Guests are less likely to remove their shoes at parties when they are dressed up, but they might still offer. They are also a little more likely to remove their shoes in winter, though shoe removal in summer is still common.
I would argue on this basis that it is perfectly fine to insist on shoes off as a rule. If you ask your guests to remove your shoes, you are simply asking them to do what most people do most of the time anyway.