I receive the benefit of Private Health Care Insurance through my employer too. It's a perk and you are only paying tax on the actual benefit .......... for example, if the cost to you as an employee is £40 per month, you will only pay 20% of tax of that (if a standard rate tax payer), the rest is free.
You are not paying "extra tax", a benefit is treated as income. it's a perk and the other 80% is free. It also doesn't include "ordinary" trips to see a GP for day to day issues or emergency treatment. This perk is used by companies to try to keep sickness levels down and the huge amount of associated hours lost