Unfortunately it is a bit of a bummer living in the CPL flight training black hole that is the North east. Quite correct, Leeds is your closest option. Nothing at Carlisle or indeed Newcastle for the MEP/IR, and Humberside is even further than Leeds. Expect a 1h45m drive to either of the schools at LBA for as long as the traffic is kind to you. Facilities at LFS are considerably less comfortable after a long drive than at Multiflight, but I can't knock the training there (although the GA7 isn't necessarily the best a/c for the job due to its lack of icing protection).
Not sure that Teesside is a complete loss though. Cleveland Flying School I am sure have twin a/c available to them and you may be able to complete the MEP rating, but I'm not entirely sure about the IR. Not an approved school for CPL training though (last I was aware at least).