There's an article about this from moneysupermarket in www.mumsnet.com/family-money/insurance-costs-for-teenage-drivers. One thing it doesn't cover is insuring your child to learn to drive.
Try Adrian Flux www.adrianflux.co.uk/extras/learner-driver/ or
Provisional Marmalade www.provisionalmarmalade.co.uk to suit you best. Cheapest by far. Surprised moneysupermarket didn't know this?