How to reply to "you ok" in British?

The reply is just:

• OK?

It's not:

• I'm doing great thanks: I got a pay rise last month ....

It would work a bit like "How ya doin?" in this video.

And here's how not to do it.

A typical exchange might be:

• A: You ok?
• B: Ok? How's it going?
• A: Yeah, good cheers ...

• B: Good ...

-

I would just say, "Gooood! You?"

Depends how it's being asked. If it's inquisitive, as in you're doing something and they want to know if you're OK. They're generally asking if you need help.

But in the situations you've described, it'll most likely be a cue to engage in smalltalk. If you say "I'm good thanks, how's things on your end?" and they stick around, it was asked to engage in conversation. In which case you should address their reply or just ask how their day has been.

Sometimes however it's said to break the awkward silence, when accidental eye contact has been made or to acknowledge your presence. In which case you can just nod or say "Fine thanks".