Generally, it is fair to expect an employer to provide all necessary equipment for someone to undertake the role they have been employed to do. If an employee is unable to work because they do not have the correct equipment, that employee will obviously be unproductive. This is not their fault and there is a risk that the employer will be in breach of contract.
Homeworking can complicate matters. Where an employer is requiring staff to work from home, they should be providing the necessary equipment for those individuals to do so in most cases. There is an argument that employees could be expected to use personal equipment, but the vast majority of business have IT and Data Protection policies which would usually ban this and for good reason. Employees will understandably be reluctant to connect personal equipment to a business network for similar reasons.
Whoever makes the request, the practicalities of working from home and going to be a key consideration and everything from the cost to responsibility from moving items from workplace to home will be relevant.