I used to think that the Brits said 'in [determiner] street' whereas the Americans use 'on [determiner] street'. I believe that's what I was taught in school. However, the other day I checked a few dictionaries and didn't found information about such a distinction but noticed both usages. So, what's the truth? Here are some example sentences from Longman.
I bought this coat at a shop on the high street. [it says it's BrE usage]
They live on Clay Street.
on the other hand
The restaurant is tucked away in a side street.
She had lived in the same street in London all her life.