Is there any way that I would be able to shadow a surgeon?

I’m not really sure what I want to do with my life career wise. I am currently studying Philosophy looking to complete a Philosophy and Psychological Studies Degree in 2012. During my studies I have become increasingly fascinated with the human brain and body in general, specifically thought the brain and heart.

I wanted to know if (in the UK) there was any way that a surgeon would let me shadow them for a week and watch their surgeries even having no medical training or background…would there be any way that you could shadow them and just watch their moves for a week?

My motive for wanting to do this would be two fold…
1) I’d really like to see what a neurosurgeon and cardiologist do in terms of actually watching their work for career purposes

but really more than anything
2) I’m truly fascinated by the human body and would love to just be able to see an open heart surgery.. to see a real heart and to see a real brain… even if I don’t eventually choose this path, I think actually seeing something like that could be really transformative…

I would imagine that people just don’t do these sorts of things unless you are a medical student, dedicated to learning the profession… but I’m just wondering whether it’s worth some well thought out letters of begging sent to a great number of surgeons…(maybe I’ll get lucky?) to enable my dream to come true…So if anyone knows anything about this specifically relevant to the UK I’d be very grateful… Thanks