Hi Mark
Do you mean "RIDDOR" reportable or all accidents?
If it is a RIDDOR reportable accident or other event, then RIDDOR 2013 tells you who is the "responsible person" is in Regulation 3:
Responsible person
3.—(1) In these Regulations, the “responsible person” is—
(a) in relation to an injury, death or dangerous occurrence reportable under regulation 4, 5, 6 or 7 or recordable under regulation 12(1)(b) involving—
(i) an employee, that employee’s employer; or
(ii) a person not at work or a self-employed person, or in relation to any other dangerous occurrence, the person who by means of their carrying on any undertaking was in control of the premises where the reportable or recordable incident happened, at the time it happened; or CONTINUES
So, if the person is an employee then the employer. If the employee is employed by a sub-contractor, then that sub-contractor, though in practice many Principal Contractors end up doing it themselves particularly if they don't fully trust their subbies (and, in some cases, simply to have a handle on how many incidents are happening under their oversight).
If the injured party works for an Agency then it will depend on their terms of engagement as to whether they are employed by the Agency or self-employed.
If the person is self-employed, the person in control of the premises, which in this case is likely to be the Principal Contractor. NOTE that RIDDOR 2013 shifted the responsibility from the self-employed who previously were required to report their own injuries with HSE research indicated that in almost all cases they didn't (Underreporting circa 90%).
There is NO explicit duty to investigate ANYTHING under RIDDOR. However, the need for investigation of RIDDOR-reportable and other incidents is implicit under HSWA and, in particular, the duty under the Management of Health and Safety at Work Regulations 1999 to review arrrangements for managing health and safety.
The Client may be in the frame so may well set out its requirements for communication of incidents on their site in Contract specifications and/or Pre Construction Information.
I would expect the Principal Contractor to set out its requirements for investigation in the Construction Phase Plab either directly or by cross-reference to other documentation.