In order to become a Social Worker you will have to complete a degree.
Have a look at the Social Work Careers website for more information about what the job involves and how to go about training:-
http://www.socialworkcareers.co.uk/
If you particularly want to work within a hospital setting, it might be worth checking out the NHS careers website (http://www.nhscareers.nhs.uk/) as there may be alternative careers that will interest you, which won't involve undertaking another degree.
Good luck!