Let's say it starts raining when you're walking. Those who put up their umbrellas immediately are foreigners, those who do not are British. I think it's quite a correct way to distingusih. You can always find someone who does not care even it's chucking it down, few parents are worried about that their children might catch a cold. The British never mind getting wet somehow.
I recall a friend travelled from Japan and stopped by London for just a few days. The friend was shocked when walking around Hyde Park on a rather heavy rain day, catching a sight of a white young man soaking wet without an umbrella eating a banana.
The man was undoubtedly a British. The eating while walking culture and walking under the rain without putting up an umberlla culture. It's normal to get shocked when witnessing these two aspects at once.
Of course there are people using umbrellas recentlly. But not using is all right though.