One of the best ways of getting work experience at hospitals is to contact consultants directly.
I have to admit that it wasn't something I was looking forward to when I posted my first letter and send the first email, but after lots of perseverance a surprising number have said yes. Even then, a few friends of mine have had run-ins with the co-ordinator here, so just watch out for people trying to assert themselves but 99% of the time the consultants will be more than happy! From my experience they have enough time to explain everything well to students, even at 16 without any clue what half the phrases mean. There will always be the one odd consultant who has a go at you for daring to ask, but most are a friendly group of people more than willing to aid aspiring young doctors.