For supply teaching, it is in most cases not possible to be self-employed. Please refer to HMRC's website for more information: https://www.gov.uk/guidance/check-employment-status-for-tax. Also note that most schools prefer their teachers to be paid as PAYE our through an Umbrella company.
If you are considering working as a self-employed teacher, it is vital to seek professional advice based on your personal circumstances. There are limited situations where this may be possible, but for most teachers, this is unlikely to be a good solution.
Please contact us on 0330 122 6629 if you have any further questions, or the HMRC Employment status helpline direct on 0300 123 2326, 08.30-16.30, Monday to Friday.