There should be legislation to regulate which ID can be demanded. Add it to GDPR which regulates how it's processed and kept on record.
As more firms seemingly bullying customers and the importance of ID, only legislation would forcibly keep open options for people and particularly prevent discrimination. If you don't have a credit card by choice, as there isn't a legal requirement anywhere to have one, it is discriminatory to require it, particularly since there are perfectly legitimate alternatives (perhaps even better) available such as the government-issued docs listed below.
A useful framework could be the one that insurers, banks and solicitors tend to use. Typically they have two categories (often called 'primary' which means photo ID and date of birth, and 'secondary' to prove current name & full address), as policy they state examples for each category, and require one item from each category, sometimes two from primary.
These days, as insurers and solicitors (both in personal experience) accept sight of docs via email attachments, so can any firm that uses electronic communication. In my recent experience, councils, phone companies and utilities do the same.
Below is just detail, skip if wished. (Most of these I knew from working for banks, solicitors and insurers, but have just googled to double-check and update.)
Most commonly accepted for 'primary' are government-issued photo-docs: current UK/international passport, current UK or EEA photocard driving licence (full or provisional), National identity card (for EU/EEA/Swiss nationals), Biometric Residence Permit (BRP) or Home Office residence permit, Armed Forces ID card or firearms certificate. While not government-issued, a current debit or credit card is often requested or is accepted if offered, but it's a supporting item unless you're applying to, say, open an account with the same firm that issued the card.
I see from the eBay discussion boards that, due to recent HMRC requirements, things like National Insurance number may now be required.
Most commonly accepted for 'secondary' , recent, in the last 3 months: utility bill (gas, electricity, water), current year's council tax bill, bank/building society statement, mortgage statement, (legal) tenancy agreement, HMRC tax notification or PAYE coding notice, benefit book or letter from the Benefits Agency. Otherwise the organisation can usually make alternative arrangements, indeed banks are required to by the Joint Money Laundering Steering Group e.g. a letter from a hospice/care home manager.
Where certified copies are required, they can be certified by (free or guess who usually charges a small fee) a solicitor, bank official, minister of religion, doctor, dentist, councillor etc., presumably somone in a role good standing. My brother-in-law had his done by his pharmacist (implausibly but appropriately named Dr Quack; I've posted about this elsewhere).
