As far as I know anyone can walk out of a job at anytime, its best to avoid that situation if you can, but you may risk not getting a reference and perhaps having to fight to get your p45 which you need for new job and also any back money due to you.
You could try to negotiate with your employer explaining that for personal and health reasons that you are unable to work out the notice period required and that you regret this very much or something like that perhaps.