I don't quite understand how it works but chemists does really survive when they are not close to and designated primary service for a GP surgery close by (and possibly get a financial incentive from the NHS). This does mean that prescriptions can be provided close to the GP surgeries.
Unfortunately Forest Hill ward doesn't have any GPs so it isn't able to keep a chemist on the high street, especially when Boots is competing against Superdrug and Sainsbury's in Forest Hill - both of which seem to provide better value for money on all non-prescription products.