The Health and Safety Executive in Great Britain is a Government body which is responsible for health and safety regulation. As part of it's duties it regulates The Health and Safety at Work Regulations. Part of these reuglations are to ensure that employers have an adequate number of trained First Aiders and tthat they have access to First Aid equipment (typically the kits you see around workplaces).
That brings us on to what is an HSE First Aid Kit?
The HSE state suggested contents lists and First Aid kits based around these lists tend to be called 'HSE' First Aid Kits. They are in no way approved by the HSE, nor are they compliant with anything other than these suggested contents lists.
The reason this is mentioned is because the employer has a duty to assess the risks in the workplace and provide adequate First Aid provision. This is covered by The Health and Safety (First Aid) Regulation 1981, so has the force of law.
For example, if you work in an environment where there is a lot of hot work, it is fair to say that you are at risk of being burned. If someone is burned and the HSE discover there was no burn treatment within your First Aid kit, they may not be too happy. Therefore, your HSE First Aid Kit was not compliant with the Regulations. They will find out because most First Aid treatments are reportable by law (RIDDOR).
To conclude, yes buy an HSE First Aid Kit (for the right amount of people) as a starting point. Add in the extra items you would need in that kit determined by your risk assesments. Then you should be compliant.
Lots more information on the subject can be found on the HSE website.