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Take bus 167 from Piccadilly Gardens, Lever Street/Dale Street (Stop E) in central Manchester, and get off at stop: Birch, Heywood Old Road/Langley Lane (journey time approx. 25 minutes). The service is hourly (more info on times from: (http://www.traveline.org.uk/index.htm). You should be able to see the services when approaching the bus stop. When you get off the bus, walk down Whittle Lane (which goes over the motorway M62), and you will be at the services, where you can hitch a ride down the M62 to Leeds or Hull. The bus costs around £2.50. You can get cheap coach tickets from Megabus or National Express funfare (they have websites) where you can get trips from between £3-6 if you book in advance. So I would only take this hitching route if you are on a low budget or traveling last minute.
Update (March 10, 2016): Bus 167 is no longer in service, however bus 163 can take you pretty close to the services mentioned above. The fare from Picadilly is £3.80 though, so doesn't much sense. Another option is to walk down the A56 (Bury New Road) and wait at the exit ramp of the ring road merging with the M60. Alternatively you can take the tram to Prestwich to get there.
=== South Towards Birmingham and Bristol ===