I reckon that although Britons as a rule wouldn't normally strike up a conversation with a stranger, the culture of "politeness" means that if found unexpectedly in a conversation with a stranger, they will continue unless they really do actually have somewhere they need to be.
I would say a lot of Brits really do enjoy talking to people, not as an obligation of 'politeness'. The culture of politeness is more likely to be a cause than a symptom. (Speaking for myself) I find it hard to talk randomly to strangers because it's imposing on whatever they may be doing at the time.
Watch for Brits asking each other for directions, or for the time, even in plain view of a clock tower. It's sweet in a repressed kind of way.
