You haven't said as much, but I suspect her 'illness' may be stress-related. Clearly her employer being awkward isn't helping. Quite frankly, I'm amazed at OH's attitude - they're usually pretty sympathetic in most large organisations. Employers can terminate employment, however, if they consider an enployee is not fit to return to her job or to any alternative job they may be able to offer her, and she may not be fit to do the job if she can't cope with its inherent stress levels.
But as Lottie says, if your friend has a sick note valid until a certain date, then it's illegal for her to be working before that date, whether or not she can 'function' (and you usually can function when the cause of the stress, i.e. work, is removed). If her employer wants her back at work and if she and her doctors are happy for her to go back, then they should be talking to her now about a phased return, possibly going back part-time to begin with, building up to full-time hours over a period of weeks. It would also include a review of her expected workload on return.
If her employers insist on ignoring the opinions of medical professionals (and many OH practicitioners aren't actually doctors), as well as the law,then she could be in a strong position to take her case to tribunal.