The Health and Safety Executive does not impose a particular number of appointed persons or first-aiders at work. The responsibility lies with the employers to determine the correct number and ensure that there is adequate provision.
In order to assess the needs of your business, you will need to take into account your type of activity as well as the number of employees that you have on site. Look at any illnesses or accidents that have occurred in the past so that you can draw conclusions and put procedures into place that will minimise any risks should the same happen again.
Once you have determined whether your business represents a high or low risk to its employees, you will need to decide on a sufficient number of first-aiders. Again, as there are no rules set in stone regarding the number of first-aiders, you must ensure that any accident or illness can be attended to immediately, whenever there are workers on site. You should also plan for any first-aider absences due to holidays or sickness.
It is always safer to err on the side of caution by providing first-aid training for more employees than strictly necessary. Not only could that decision save lives, but the HSE will prosecute companies if they put employees at risk or fail to comply with the law.