The specific answer to your question is that there is no explicit duty to investigate accidents, but there are "implied" duties:-
1) Implicit duty under Regulation 5, Management regulations i.e.. Arrangements for monitoring of the preventive and protective measures.
Previously, the ACoP to the Management Regulations in para 36 under Regulation 5, Health & Safety Arrangements; Monitoring :-
Employers should measure what they are doing to implement their health and safety policy, to assess how effectively they are controlling risks, and how well they are developing a positive health and safety culture.
Monitoring includes:(b) adequately investigating the immediate and underlying causes of
incidents and accidents to ensure that remedial action is taken, lessons are learnt and longer term objectives are introduced
2) Implicit duty under RIDDOR for those that have to be reported to HSE, as one cannot adequately complete part, "About the Kind of Accident" i.e Describe what happened (give as much detail as you can, including i) the events that led to the incident ii) the operation or activity in progress. Describe any action taken to prevent similar incidents occurring).
Last, but not least, extract from HSE Guidance, "Investigating accidents and incidents:
A workbook for employers, unions, safety representatives and safety professionals -HS(G)245
http://www.hse.gov.uk/pubns/hsg245.pdfLegal reasons for investigating
To ensure you are operating your organisation within the law.
The Management of Health and Safety at Work Regulations 1999, regulation 5, requires employers to plan, organise, control, monitor and review their health and safety arrangements. Health and safety investigations form an essential part of this process.
Following the Woolf Report on civil action, you are expected to make full disclosure of the circumstances of an accident to the injured parties considering legal action. The fear of litigation may make you think it is better not to investigate, but you can’t make things better if you don’t know what went wrong! The fact that you thoroughly investigated an accident and took remedial action to prevent further accidents would demonstrate to a court that your company has a positive attitude to health and safety. Your investigation findings will also provide essential information for your insurers in the event of a claim.