Out today with DH and DS in buggy on the high street. We were waiting to cross a junction and the driver kindly stopped to let us cross.
I waved a thank you, and slightly ran to get across quicker.
DH waved and strolled at normal walking pace.
I was surprised at this and said that I think it's polite to run across so you are not holding the person up any longer than you need to when they have politely waited for you to cross the road. DH said he felt that waving a thank you was sufficient, there was no need to run.
Typing this all out it all sounds awfully trivial and like a British problem but genuinely interested in what other people think about this!