I think everyone knows the world's favourite rodent. Mickey Mouse is generally used as a rhyming slang for "Scouse" as a person from Liverpool.
So why 'scouse'? Lapskaus is a Norwegian stew that became a staple diet of sailors, as a port town Liverpool had lots of Norwegian sailors and Liverpudlians being friendly types can't resist trying a bit of scran (from Romany for scraps (of food) and used since the 18th century, again especially amongst sailors/Navy). Lapskaus eventually became scouse and a staple of the Liverpool diet and remains so to this day. The unusual yet charming name also attached itself to the region's distinctive accent (there's also a largely unique slang vocabulary that's a language of its own) and later to the people.
Hence a Mickey Mouser is a scouser or person from Liverpool.
So a sentence would be: "I went to uni in Liverpool and was friends with some Mickey Mousers even though I'm a Manc" which translates to "In my two weeks at university in Liverpool I was friendly with some Liverpudlians, despite being a Mancunian"