Just been looking for a new phone for my daughter and came across the u-fix deals from t-mobile... which means she can't run up huge bills !!
I believe the u-fix deals have been running for a while (u-fix is a contract that doesn't allow you to go over you're allocated minutes without buying additional credit), but they've recently added free internet if you buy the sim from their web-site and go for the minimum £20 per month contract. £20 gives you 600 minutes a month and unlimited texts.
These are also on a 30 day rolling contract, so can be cancelled at any time.
This is perfect for teenagers, because it gives you (as a parent) peace of mind that they have sufficient credit but without the hassle of continuously buying top-ups.