The law says that you may self-certify your illness for seven days before any need for an official document.
The Statement of Fitness for Work, or 'fit note', is a Medical Statement that GPs issue after a period of absence from work of greater then seven day. It replaced the old 'sick note' and aims to focus on what an employee may be able to do at work rather than what they cannot do.
If you require a fit note please see a doctor.
If you require a 'sick note' for an illness of fewer than seven days duration, a private doctor's statement may be requested. The fee for this is £15, which is a set BMA rate, to be met either by you or your employer.