Vector 361 - there's no such thing in the UK, can't speak for ICAO
In the London TMA 3 miles separation is subject to a host of other conditions - below FL245, a minimum distance from the radar head (depends on the radar source) , identified and talking to a co-located controller with a rapid means of co-ordination.
However approach controllers can use 2.5 nm on base leg and final within 20nm of touchdown and I understand that is ICAO too.
From your post it seems that it's common in the US to allow aircraft to be on their Own Nav 3nm from each other? Maybe we're overly cautious but it wouldn't happen here - at least one and usually both would be on headings if that close.