A 'Fit for work' certificate (fit note), which replaced the old sickness certificate (sick note), will not be issued for any illness lasting seven days or less. Your employer may, however, require you to complete a self-certification form (SC2), which is available from your employer (or by complete online here).
For any illness lasting longer than seven days you will need to see your doctor for them to issue your fit note / sick note. Subsequent renewals may be possible by telephone - your doctor will advise.