This is a good question and it's actually where the British weather can play a valuble part.
The key to learning better cornering is to learn to feel what the bike is doing underneath you and to learn what it feels like to break and correct traction and to feel confident with the bike drifting underneath you, i.e. both wheels sliding equally and in a controlled way around a corner.
When you have loads of grip, the speed you need to acheive that is very high. Consequently if you come off the chances of you hurting yourself are higher.
So, what you need is wet weather and a suitable, loamy, loose corner with a small berm on it. Depending on where you life that will be easier or harder to find - in the SE there's loads but ooop north and at trail centres, in the peak district they are harder to find because the trails to be rockier.
With the wet weather your tyres break traction much sooner and thus at lower speed, so you can practice getting a feel of the bike moving around and breaking traction and you can experiment with moving your weight forwards and backwards. All this can be done in relative saftey because you're not going to be travelling that fast.
To enahnce the learning, drop the saddle by a good amount, say three inches or more as this will allow you to drop your centre of gravity and have more control. Also try to experiment using flats as you will innevitably want to drop a foot at some point in order to stay on the bike.
Weighting up the front tyre is a key skill, which means moving your weight forwards to give it more grip. The back end can break traction without causing too many problems for you but it's materially harder to rescue a bike when it's the front wheel that's loosing traction.
Try approaching this loose/loamy corner in the wet, breaking before you turn, then moving your weight slightly forward as you turn in to weight the front wheel. You'll feel the rear go a little light and probably slip at which point you want to dig onto the outside pedal, drop your inside shoulder and push the bike around the corner with you shoulders and hips.
That's hard to describe and you'd be better off getting some coaching from Jedi or something. But the wet weather practice is the best way to learn the basics.
