You need a birth certificate to get a passport [1]
You need a passport to get a driving license [2]
In order to vote you need a national insurance number [3], which is issued to you on your 16th birthday, via your guardian's/parent's electoral registration information.
Ergo a birth certificate is a de-facto national ID (or immigration documents)
[1] https://www.gov.uk/apply-first-adult-passport/photos-and-doc...
[2] https://www.gov.uk/id-for-driving-licence
[3] https://www.gov.uk/national-insurance/your-national-insuranc...
I don't have a british passport, a british drivers license, but I do have a NI number. I can vote, I can open bank accounts, I can get amazon parcels, I can do normal daily things without them. The only people who have my NI number are 1) the electoral register, 2) my employer, and 3) hmrc (as far as I'm aware at least).
I've not shared it with Amazon (who are the company mentioned in the post), or with my utility provider, or with my broadband provider. I've also not given them my passport or drivers licence, and yet they all seem perfectly capable of verifying I am who I say I am, all without me having any form of national ID.