The season on rivers does not start until June 16, but (many) stillwaters are open all year round. The lakes and gravel pits in the Trent valley are worth a shot, especially the ones close to the Trent itself because when the river floods, the fish find themselves washed into all sorts of places, including the lakes
This could be one reason for the Trent`s population of large carp. I have caught many stillwater (and river) chub and found that whilst the river chub could be caught on all manner of flies, especially large bushy dry flies the stillwater fish were easier to catch on lures such as a 5 gram black and gold original floating Rapala minnow (best chub lure ever imho

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Your best bet would be to do a search on the computer for angling clubs in the area you are visiting Shad and drop them an e-mail for info. Hope this helps a little,
Good fishing,
Andy.