You only require a sick note if you have been off for more than 7 days. For the first 7 days of illness, you are required to complete a self certification form. GPs are not allowed to issue medical certificates for the first 7 days of an illness.
If your employer insists on a medical certificate for the first 7 days, a private sick note can be issued by the GP. Please not a charge will be made for this.
If you do not qualify for statutory sick pay or statutory sick pay runs out and you are still unwell, you should ask your employer to complete form SSP1 and send it to the local JobCentre Plus to claim for Incapacity Benefit.