Your employer should provide you with a self certification form which covers your first week off sick. NI certificates (form Med 3) are only available from your doctor and commence after one week of absence from work. If your employer requires a private certificate, a standard fee will be charged. Hospital wards and outpatients are able to provide routine certificates.
If you're off work sick for more than 7 days, your employer will usually ask for a fit / sick note (or Statement of Fitness for Work) from a GP or hospital doctor. Fit / sick notes are sometimes referred to as medical statements or a doctor's note.