It needs to be appreciated that the UK Government, in its wisdom, has not included every possible type of benefit in the definition of Public Funds, as in para 6 of the Immigration Rules. Again I state that there is absolutely nothing health-related in that definition.
In order to check for yourself
click here and then scroll down to para 6, which you will see is just a list of definition, including the one you want .... Public Funds.
Again, claiming free NHS prescriptions or free NHS dentistry ..... if there is an entitlement .... is not within the definition of Public Funds. No problem claiming. In particular, a woman who is pregnant, or has given birth in the last 12 months, is entitled to claim these benefits .... and should!