Medical insurance is free but the benefit is taxable?

My employer's offer letter states that they provide free private medical insurance. At the same time, there is a sentence saying the taxable benefit rates for healthcare for a family are £960/year. I assume my employer pays my premiums for me, and if he pays premiums over this amount, then I am responsible for paying taxes on the excess amount? How would I know what my employer is paying in premiums?

Please clarify if you are in a similar circumstance.

Yes you are responsible for the tax on the insurance.  Your employer will issue you a P11d each year showing how much is taxable.  It's taxable in the UK, but it's tax-free in the US.