Spend time sitting in the Courts of Justice in the Strand. You can sit in any of the courts and listen to senior judges trying fascinating cases. There's an excellent canteen where you can get a reasonably priced lunch, and you'll learn things about the law, and the way it's administered that will broaden your horizons. You'll also learn a great deal about human nature.
It's free, apart from anything you buy in the canteen, and the time will fly by.