I've been associated with private training in manchester/liverpool area for around 4 years. Barton are good and advantage of being at the airfield, therefore no landing fees, however, they are on grass and therefore the field is often closed due to water-logged. Also, their training costs are high as they have no competition.
I have done a lot of training with MFS at Manchester and think that they are very good and very professional instructors, esp 2 of them (I will give names if you want). However because of the high overheads they are expensive (£128/hr & £15 landing fee). In addition you are restricted on the hours you can take-off/land, after 11 and before 6 on some days.
I would however strongly recommend Liverpool. This is a training airfield therefore the competition is high, therefore lower costs. Ravenair are very good (flown with them) however Liverpool Flying School are excellent, very professional and cheap (£82/hour) on a PA-38.
As I say, I have been associated for about 4 years, therefore know quite a bit, drop me a PM if you want anymore info.
Good luck
Craig