Yes. Health and Safety Executive (HSE) recommendations state that it is good practice for first aiders and appointed persons to record incidents that required their attendance. The information can help identify accident trends and possible areas for improvement in the control of health and safety risks. It can also be used as a record in future first aid needs assessments. A first aid record book is not the same as a statutory accident book, although the two could be combined.
Accidents may also need to be reported to an enforcing authority under the Reporting of Injuries, Diseases and Dangerous Occurrences Regulations 1995 (RIDDOR). (See What kind of accidents should I report?) Employers must report deaths, major injuries, injuries or diseases that involve being off work for more than seven days, and dangerous occurrences if they "arise out of or are in connection with work". This includes violent incidents.