Unlikely to be it since it’s nowhere near from the last 10 years, but CITY 2000 seems like it could be similar at least artistically?

I think the best I can recommend is looking through Steam, searching for “London” and the mystery genre. I didn’t quite catch anything there that fit at a glance, but maybe you will. Similarly could be done on GOG, since it sounds like it could potentially be an older game? Or itch, but maybe the best way to search for that would be by googling london missing friend mystery site:itch.io.

I’m assuming a modern setting, with no supernatural elements and the mystery genre, so that’s the best I could do. It’s going to be very hard to find something without some details being fixed. Point and click? Photos or isometric? Is the player character visible? Do they have any identifying details? Does the pub have a name? Anything like that could do a lot.

You say you watched someone play it on youtube then you might be able to search your youtube viewing history?