If you are being advised by an official source.. gov.uk, it would be prudent to follow the guidance as set out.

In reply to Martyn:

I don't work in a School or Academy but when we check a UK/Irish citizen and they don't have a passport, we ask for a scan of the electronic evidence showing which organisation has issued it. Even the Home Office has moved to online checking for all non UK/Irish nationalities so no hard BRP stamp in passport any more; we have to take a scan of the email the Home Office sends to an individual confirming their visa application has been received and is being processed as part of our RTW checks for overseas nationals.
As some point, they are going to digitise UK and Irish passports so we can do online share code checks for this group too.

Hi, I am also not in a school or academy but I hope this will help -

I recently did a RTW check in preparation to issue a CoS for a potential employee on a Graduate Visa moving on to a Skilled Worker visa. Following gov.uk advice I requested from the individual, and ran their ‘share code’ and date of birth alongside some of our organisation’s details (gov.uk needed the details to keep track of the RTW checks). An electronic verification with mandatory details (including photograph!) of the applicant was immediately made available to us.
As Helen mentioned, no passport stamps, BRP etc would prove valid.

Again, not in schools so requirements might be slightly - or vastly - different.

Best wishes!

In reply to Martyn:

Thank you Martyn. I suppose my question really is Can an "official letter or document" from a previous employer be electronic?

In reply to Alex:

I have used electronically generated P60, P45 and wageslips as evidence of NI number before. The are all "official" as they are connected with PAYE. If you are concerned about due dilligence then you could always contact the previous employer to ask them to confirm they are genuine.

In reply to Jim:

Thank you Jim.

Hi Alex,

To conduct Right to Work checks, individuals from the UK and Ireland must present their passport or passport card. Beginning April 6th, 2022, individuals from the rest of the world will need to provide a share code. Additionally, there are individuals who possess EU settlement documents and right to indefinite leave. For these individuals, you need to verify and document their status accordingly.
To ensure that you have the correct documentation, I advise you to refer to www.gov.uk/legal-right-work-uk.
If an individual cannot provide the documents mentioned in the checklist, you should check with the Home Office. Commonwealth citizens who do not have the right documents may still be eligible to work in the UK.

Thanks.

Hi Alex, as most of the replies have missed what you're asking allow me to provide some advice. A P45/60 is acceptable alongside a birth certificate for UK/Irish employees with no passport. To establish the statutory excuse you'll need to conduct a manual check, the advice in the Home Office guide for employers is to write words similar to the following on the document "this right to work check was undertaken on (date)". You could do this electronically or by hand if you print it off. Remember that you'd need to see the original birth certificate in person as well. If you have any queries ring the Home Office advice line, they're fairly helpful. I realise that this thread is several months old, but leaving this comment in case future people stumble across this post.