In principle yes the injured should complete the record.  But remember that the purpose of the BI510 accident book is related more to social security and benefits than it is to RIDDOR or general accident recording and reporting.  I would expect that you would have internal recording, reporting and investigation systems and not solely relying on the BI510 as your only means of record and report.  I would expect your internal procedures to identify if it was a true report and if it turns not to be the case then offer the injured person the opportunity to make a second entry themselves or amend the existing entry.  Any repercussions as you put should really arise from your internal reporting and investigation procedure.  One action you may want to take is to doing a bit of training with your first aiders to remind them what their responsibilities are.

There was a separate post on signing accident forms (during the GDPR furore) - the HSE accident book was revised at the time of Data Protection with the signature giving permission from the IP to share the information from the record with for example Trades Union Health & Safety Representatives, not to confirm an entry

Trouble is that where people have evolved their own in-house form rather than paying for accident books they may have miss-interperted the purpose of the signature

Despite background issues with the forum pages I have located the relevant text from BI510 second edition question 4

For the employee only By ticking this box I give my consent to my employer to disclose my personal information and details of the accident which appear on this form to safety representatives and representatives of employee safety for them to carry out the health and safety functions given to them by law.

Followed by signature and date

Edited by user 06 July 2018 20:14:25(UTC)  | Reason: adding signature comment

Originally Posted by: shecar

Thank you. for your advice - my major concern was that the 'injured party' was not aware of the report and that the report may not be factual. Unfortunately it seems that there has been no follow up or investigation by the previous H&S Advisor - this is something I will have to deal with some 8 weeks after the event!

That puts a different complexion on it altogether.  I think you need to address training of your first aiders and look at your first aid and accident procedures and policies.