I think this is British usage - in America everything is on streets, avenues, boulevards, circles, squares, etc. "We live on South Street. His father works two miles away, on St. Charles Avenue. His grandmother has a lovely home on Washington Square."
As for walking, "walking the streets" does not necessarily have a sexual meaning, although "streetwalking" certainly does. You could say "I walked the streets for hours looking for my lost dog." Here, "in the street" means literally on the pavement of the street: "Our kids have to ride their bikes in the street, since there's no sidewalk in our neighborhood."
Here are some walking examples (AE):
He walked along the streets downtown, looking at the boarded-up buildings.
She walked down Grand Avenue, took a right, walked two blocks on 2nd Street, and came back up Filmore Street.
If you go for a walk downtown, be sure to stay off Montrose Street - it's not safe after dark.
Tourists often spend time walking up and down/along/on the famous Miracle Mile.
Hope that helps...
[not a teacher]
Student or Learner