All destinations served by Barcelona's (wonderfully-named) El Prat airport, together with the relevant airlines, are listed here:
http://www.aena.es/csee/Satellite?cid=10455696 07363&pagename=subHome&Language=EN_GB&SMO=8&Si teName=BCN&c=Page&MO=1
(That's the first of 6 pages. Click through the links, at the top of the list to see more destinations).
That list shows easyJet as the only operator ex Liverpool. It also show that both Monarch and British Midland (bmibaby) fly from Manchester:
http://www.bmibaby.com/bmibaby/en/index.aspx
As Mushroom25 indicates, Ryanair serve Barcelona via bus links from Girona (which is served from both Liverpool and Manchester) and Reus (which is only served from Liverpool). The non-stop buses take just over an hour, from either airport, into Barcelona city centre.
Chris