If you're happy to go by coach most of the way, here's a slightly off-the-wall option, albeit one which requires an early start.
Train: Leeds to Bradford £3.30 Anytime Single
Thandi Express Coach
http://www.thandiexpress.com
Bradford to Gravesend £24.00
(coach leaves from Bradford Metro Interchange Bus Stn at 0725 arriving at Gravesend Khalsa Road at 1345: there is also an afternoon departure but it's no use as the ferry to Tilbury has stopped running before the coach arrives in Gravesend)
Walk to Gravesend West Street Pier
Tilbury Ferry (every half hour, last departure 7pm) £3.50 single
Total £30.80
One definite catch: the stop in Gravesend isn't that near the pier (a 15 min walk - not ideal with luggage; maybe a bus or taxi would be advisable for this bit.
Other possible catch: I've no idea what Thandi's reputation as a *coach* operator is like. I do know they had a fairly (and I think consistently) shocking reputation when they formerly dabbled in *bus* services - certainly in Surrey (near Heathrow) and I think also in Birmingham
If you do go by train (as in all honesty I would inclined to be), I think that any train ticket to Tilbury Town will be issued to "Tilbury Stations", and as such is valid on the connecting minibus to Tilbury Riverside (Clintona Coaches route 99) from opposite Tilbury Town station - make sure you leave by the correct exit, the one on the platform you should arrive on from London, on Dock Road.
One small correction to something tgsg2011 stated above: if you touch out at Grays you need not necessarily have to wait half-an-hour for the train to Tilbury. Tilbury only has two trains an hour from London, but Grays has four (two via Ockendon, two via Dagenham Dock). If you arrive from London/West Ham via Dagenham Dock at Grays, for most of the day it's a 17 minute wait for the Tilbury train.
