Leeds also has a large Irish population. In fact I always thought it STUPID that pub companies opened Fake Irish theme pubs in Leeds and Bradford when half of the landlords of real pubs in the two cities were already Irish. It is possible to find music of various types in the region. The Grove has official sessions on various nights including the folk stuff and also a Bluegrass session on the last Thursday of the month, but also unofficial music happens in some of the side rooms.
A pub called the White Hart (or Stag - I can never recall which) has Irish sessions at least once a week, possibly more. That one used to be frequented (probably still is) by some excellent musicians such as Tom Napper, one of the country's most accomplished Tenor Banjo players, and a really nice bloke.
The Irish Centre on Leeds Road has concerts including some of the top Irish folk bands.
Bradford, Huddersfield and York are also just a train ride away (different trains). Last train from Manchester via Bradford departs Manchester around 11pm and gets to Leeds around Midnight.
Once you find one place to go, use word of mouth to find out where the people there get to. Most of it will not be advertised in magazines.
Quack!
GtD!