A better colloquial translation of "man zǒu" would be "take it easy".
Of course, most people don't really know what they mean when they say it—but their intent usually lines up with the paragraph above.
When I moved to the UK was the first time I was introduced to "how are you doing?" followed by someone walking straight past me without waiting for a reply. It took me months of replying after someone and getting annoyed at how rude they were before it sunk in that "how are you?" in the intonation commonly used, is not a question but a greeting, and that it was most certainly not an invitation to start a conversation.
Basically you can't tell without considering intonation whether these utterances are just pleasantries, or heartfelt statements and questions.
I found it very enlightening to play with intonation a few years back when talking to shop assistants. You can give a flat "how are you?" that everyone interprets as a greeting, and just keep talking. But just a slight intonation change followed by a pause, and suddenly you get near total strangers pouring their heart out to you about their day.
Same thing goes for things like "take it easy". Throw it out, and it's just a bland pleasantry. Pause and go "take it easy" and pause again while looking at someone, and it totally changes character.
I think that delivery matters much more than the actual words.
But even in London you'd be surprised at how friendly reactions you can get when approaching total strangers as long as you're to the point about why you're approaching and particularly makes it clear you don't want to sell anything (or collect money).
Your downfall if approaching strangers in London would be if you think you can do it slowly and casually and start with pleasantries, because perversely that has come to imply you're trying to butter people up prior to a sales pitch, whereas genuine approaches now are forced to be direct and straight to the point. That works, and gets friendly reactions.