"social welfare" in the UK normally refers to benefits (aide sociale).
The kind-of equivalent of the sécu in terms of healthcare is the NHS. For healthcare, you don't have to get reimbursed because it is "free at the point of access" (you don't pay at all).
You do have to pay for dental care. If you go to an NHS dentist - and sign up as an NHS patient, some also take private patients - it is already subsidised. For example, a check up is £21.60 on the NHS, but for a private patient it could cost £50 or more.
Prescriptions are also free in Scotland. If you lived in England, you would have to pay £8 per item (so again, subsidised already rather than a refund)