Hi there,
I'm from Leicester and can suggest Beedles Lake, its big with plenty of swims, been restocked recently and has carp to 35lb. Lots of the fish will be doubles because of the stockies but a good few 20's and i believe a couple of 30's. Cheap season or day tickets - a good water for gaining experience.
You could look up Broome angling club, they have a few waters around the county, and Willesley has already been mentioned.
Charnwood water worth a look, sand pit syndicate on the A46, Frisby pits, Murphy's syndicate, Tommy Ted's syndicate nr Loughborough.
Gilmorton Mil Farm, day only day tickets, worth a shout - some good fish in the bottom lake.
Lots of water on the Council Run Watermead complex, seen some big-uns in there and no pressure.
I fish in Northants and Peterborough now and have also fished in Notts - an hour by car and you open up a whole new world of specimen waters to go at.
Have fun
Cheers
Kev