If you have had an illness which has lasted seven days or less you do not require a doctor's sickness certificate. Your employer may however require you to complete a self-certification form (SC2) which is available from your employer or on the HMRC website.
Evidence that you are sick: If you are sick for more than seven days, your employer may ask you to give them some form of medical evidence to support payment of SSP (statutory sick pay). It is up to your employer to decide whether you are incapable of work. A medical certificate, now called a 'Statement of Fitness for Work’ from your doctor is strong evidence that you are sick and would normally be accepted, unless there is evidence to prove otherwise. You could also provide evidence from someone who is not a medical practitioner, e.g. a dentist. Your employer will decide whether or not this evidence is acceptable. If your employer has any doubts, they may still ask for a medical certificate from your GP.
For more information see the DirectGov website (where this information was sourced).