Yes
You are covered for liability insurance under your policy in respect of any employee
Contact your insurer or broker if you want confirmation but your policy document will confirm it anyway,
Would it not be a bit unusual to have "employer's and public liability" insurance on a dwelling house, which I believe is what OP needs? This cover would seem more appropriate to a commercial premises with employees and public in situ regularly?
It is not clasified as Employers/Public Liability by Insurers.
It is clasified as personal liabiliy for example it is quite usual for someone to come to your house to cut grass clean windows e.t.c. you don't have an employer/employee relationship with that person and all the legal responsibilities responsibilities that entails but you still have a responsibility if that person is injured whilst carrying out work on your property.
That is why liability cover is provided under your household policy