The easiest way is if you know someone working there - who you may be able to shadow for a few days. However, if you don't have a contact you can try asking your local GP surgery/ hospital/ nursing home/ pharmacy/ etc. to ask about work experience. Depending on your age and how long you want to be there for, they may be able to offer you something.
Remember that since medicine is so competitive, it is really hard to get work experience within the NHS. Perhaps look into volunteering in a caring role - for example in an old persons home, with kids in a scouting group, etc. - this may be slightly easier to get, cater more to what you want to do, and give evidence of a longer term commitment to medicine/ nursing/ social work/ childcare/ whatever else you're interested in as well as demonstrate your ability to show initiative and go out of your way to help others.