Can they legally do this as I am under the impression that an employee cannot work while signed off?

An employee can work whilst recovering from illness as long as their doctor agrees, as they should not do anything which could delay their recovery.

If the employee has a fit note which recommends working from home as part of a phased return to full time work then the first thing to do is ensure that the employee really is well enough to do some work.

Clearly define and agree with the employee what tasks will be done and what hours will be worked. Agree targets for how much work should be completed and pay at the normal rate.

Check your employer’s liability insurance covers you for someone to work from home and also take some advice as to whether a Health and Safety risk assessment is required for a home worker.