You do not require a doctor's sickness certificate 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 the HMRC website.
Evidence that you are sick...
If you are sick for more than seven days, your employer can ask you to give them some form of medical evidence to support payment of SSP (statutory sick pay).
Your employer can ask you to confirm that you've been ill. You can do this by filling in a form yourself when you return to work. This is called self-certification.
If you're sick and off work for more than seven days, your employer will probably ask for proof of your illness. Most employers ask for a fit note from your GP.
However, this will also depend on your employer's company policy on sick leave (or sickness absence). This policy should tell you how many days you can be off sick before you need to provide proof of illness or a fit note.
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.