I don’t think so, no. This is how it works today: https://www.gov.uk/check-job-applicant-right-to-work

If your new hire is a British or Irish citizen, you ask for their passport on their first day and retain a photo/scan. In most cases this means that a layperson has to verify that the (possibly foreign) document is genuine, but I don’t think fake passports are a statistically meaningful problem.

If they have a visa or, probably most likely in recent years, EU right to remain, they will have a share code for online verification. That takes you to a page with their details and a passport-style photo that you can download as PDF for your records.

Identifying whether someone has the right to work has never been a problem. If somebody is working illegally, it’s because the employer is either knowingly employing them illegally, or doesn’t care/bother to check (or even know that they’re legally required to do so – a perennial problem with early stage startups in London, in my experience).

Except there's no obligation to have a passport.

That says if you don't you need a birth certificate and an official letter showing a national insurance number. I guess the new thing would substitute for that?