Hi Nick,
The river Sence has been taken over by a club and worked on/stocked from Shackerstone dowstream. If they are still taking new members be prepared to pay £££s. The upper stretch is tiny, but may hold a trout or two. Find out who the landowner is and give him a call. He may be happy to let you fish in return for a bit of work, or just keeping an eye on the pheasants in Autumn.
For inexpensive fishing the canals are good. The Ashby canal around Snarestone is coarse fishing, with a few suprises

. That costs something like £15 for the year from the Measham AC. We tend not to shout about good fishing spots on here, but if you talk to any of the lads fishing they'll tell what's in and where to fish. It can be fished with fly as long as you can roll-cast. I've had most species out of there on fly, apart from carp.
The river Soar around Leicester sounds an interesting fish too. Have a browse on the forum and look for posts from Skateboard Dave who is something of an expert.