A sick (fit) note is a legal document.
For the first week, you do not need a doctors fit (sick) note for any illness.
Your employer may however require you to complete a self-certification form (SC2) which is available from your employer or on the HMRC website.
After that, a ‘fit (sick) note’ is required and must be signed by your GP (or hospital doctor); or some pharmacists (called ‘clinical pharmacists’) which are then counter-signed by doctors.
But you do not always need to see a doctor (or pharmacist) in person to get one. They look like this. There is more information on them on the NHS website here.
If your employer agrees, a similar document can be provided by a physiotherapist, podiatrist or occupational therapist instead. This is called an ‘Allied Health Professional (AHP) Health and Work Report’.