High Street is a name for the most important shopping street or main thoroughfare in UK convention. I've never been to a place that had 2 high streets and certainly not 2 called High Street. [Many towns in Scotland have a sort of quadrangle of main shopping streets it seems - one is often part cobbled and called Market Street]. If an area/town/village has multiple streets of equal worth then they might be termed North and South street or named for a building like Church Street or such.
In the past having name collisions would simply be a terrible convention, nowadays we have regulations that prevent it from happening with new names (same for housing).
The Scottish village I grew up in had a High Street - but it wasn't the High Street in the sense of "most important shopping street" (or indeed in any other sense). The "most important" street was Church Street - which even had a shop and a church, whereas High Street only had one church. :-)
High Streets can also be overtaken by events. Edinburgh's High Street hasn't been the most important street for anyone other than tourists for a few hundred years.