Oh yes you have and oh yes you can.
The landowner ownes the fishing rights up to half way across the river. This is what he is licencing to your club, ergo you have the fishing rights to halfway across the river.
I know anglers tend to fish the far bank if they can reach it, but that's angler's for you - give 'em an in and they'll take a mile.
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Similarly, you have a stretch of river 'er indoors and I walked on Sunday. Back in the 19th century, an association fished it for 12 years without permission and without being moved off and then claimed the fishing rights as their own through adverse occupation. The land was then sold during the Great War and the present landowner won't allow the association to fish from the land as they'd be trespassing. They can, however, fish from a boat not moored to the land is they would then be over their fishing rights, but only on one side of the river. On the other side the landowner there would chase them off.
Great fun!