I've checked all of the usual ways of getting fares down (e.g. buying separate tickets for each stage of the journey). Unfortunately, there don't seem to be any great savings to be made. If you're just going for the day, you can save �1.70 by buying a Cheap Day Return (assuming that you're travelling after the morning peak) to Doncaster and a Standard Day Return to Leeds. This reduces the total fare from �23.60 to �21.90.
Otherwise you'll have to consider the bus. Service X1 runs roughly hourly and takes you over the bridge to Hull. (Journey time = 1 hour). The X62 also runs roughly hourly, with a journey time of 1 hour 35 minutes, between Hull and Doncaster. Timetables are here:
http://www.yorkshiretravel.net
I've looked into the possibility of taking a bus to Hull and then a train to Leeds but it seems that this is likely to cost at least as much as taking the train from Grimsby. Unfortunately, National Express has no suitable services either.
Chris