I use my iPhone for multiple hours a day for work and play. I don’t have a single issue.

You see, it isn’t pedantry when still nobody knows what the question is.

I don’t think OP’s question wasn’t about browsing anything, particularly as they won’t clarify.

I think what they actually meant to ask was ‘Can a Watch connect to the internet without my iPhone physically with me?’ to which the answer is yes, as long as you get the cellular version.

What does ‘browse the internet’ mean?

The BBC is funded by a licence fee that is paid by people in the UK, so it’s only available within the UK.