The following text is taken from the Health and Safety Executive website and provides an excellent summary of the situation as regards workplace first aid legislation.
Employers are required to carry out an assessment of first-aid needs. This involves consideration of workplace hazards and risks, the size of the organisation and other relevant factors, to determine what first-aid equipment, facilities and personnel should be provided.
If you are self employed you are required to ensure you have such equipment, as may be adequate and appropriate in the circumstances, to provide first aid to yourself while at work.
You should make an assessment of the hazards and risks in your workplace and establish an appropriate level of first-aid provision. If you carry out activities involving low hazards (eg clerical work) in your own home, you would not be expected to provide first-aid equipment beyond your normal domestic needs. If your work involves driving long distances or you are continuously on the road, the assessment may identify the need to keep a personal first-aid kit in your vehicle.
Many self-employed people work on mixed premises with other self-employed or employed workers. Although you are legally responsible for your own first-aid provision, it is sensible to make joint arrangements with the other occupiers and self-employed workers on the premises. This would generally mean that one employer would take responsibility for first aid for all workers on the premises. HSE strongly recommends there is a written agreement for any such arrangement.