You will need to pay for those. As you mentioned, you are not allowed to accept public funds and this would fall under that category
Who is entitled to free prescriptions?
You can get free NHS prescriptions if, at the time the prescription is dispensed, you:
•are 60 or over,
•are under 16,
•are 16-18 and in full-time education,
•are pregnant or have had a baby in the previous 12 months and have a valid maternity exemption certificate (MatEx),
•have a specified medical condition and have a valid medical exemption certificate (MedEx),
•have a continuing physical disability which means you can't go out without help from another person and have a valid MedEx,
•hold a valid war pension exemption certificate and the prescription is for your accepted disability, or you
•are an NHS inpatient.
You are also entitled to free prescriptions if you or your partner (including civil partners) are named on or are entitled to an NHS tax credit exemption certificate or a valid HC2 certificate (full help with health costs), or you receive either:
•Income Support,
•Income-based Jobseeker’s Allowance,
•Income-related Employment and Support Allowance, or
•Pension Credit Guarantee Credit.
Find out more about the NHS Low Income Scheme (LIS).