CofE do exorcisms too. There was a drama series on telly a while back, based on a book, called 'Midwinter of the Spirit'. Anna Maxwell Martin starred & I read the book. Most weird, can't say I enjoyed either much but years before, Martin Shaw starred in a series called 'Apparitions' which I thought was really good, suspending reality for a bit of course because I don't actually believe in possession.
From what I've read exorcisms are low key events & only carried out when all else (mental illness) is excluded. Nothing like dramatisations. It's possible someone could feel better afterwards I suppose, if they were deeply troubled and everything else has failed.