Your employer should visit your home and carry out a risk assessment. The Institute for Occupational Safety and Health (IOSH) has published this useful risk assessment checklist (PDF, 1MB), covering your workstation, lighting, heating, ventilation and security.
Employers of homeworkers are only responsible for equipment they supply and not for equipment owned by the worker.
If you work from home doing more high-risk activities, such as manual work, working with adhesives or soldering, your employer must ensure it carries out a much deeper and more detailed risk assessment, properly addressing all the specific risks involved.
This includes making sure personal protective equipment (PPE) is correct and in good condition, with scheduled maintenance programmes. The employer is responsible for supplying and maintaining PPE, just as if you were working on the employer's premises.
The HSE has advised all employers to consult its guidance and to continue keeping records of their risk assessment of homeworkers.
If a home inspection takes place, the employer must give you prior notification.
The HSE has also produced guidance on lone working (PDF, 168KB).