Going invisible is not easy.
Also if you haven't lived on the streets you'll not appreciate how many times and for what you need ID for.
As BP says, it's all about the money.
Get work which is not cash in hand i.e. PAYE, you'll need a national insurance number or P45 & a previous employer.
All to be check-able by phone minimum.
Self employed, sub contracting, national insurance and self employed certificate.
Drive a car?
Insurance, tax, driving licence?
In today's CCTV computer world, they are linked and one scan by the right camera or a nosy plod will bring unwelcome attention.
Medical services?
National insurance number / nhs number.
Even if you lie, all computers and databases are being linked.
Anything more than casual medical treatment and you'll get flagged.
OK not fully working throughout the country BUT can you afford to slip up.
Accomodation.
B&B, motel, private room, probably ok.
Letting or buying a property, no chance.
You'll need a bank account, photo id, deposit, and probably a national insurance number. Not forgetting references if you are too young.
Bank account.
Birth Certificate, Photo ID, utilities bill, proof of address, and depending on how old you are, references. National insurance number, and P60 even.
Post?
Even if you think you can just general delivery your post, you'll need ID to pick it up.
Photo ID so that's a driving licence or passport, or in date utilities bill.
You'll need an accommodation address.
You'd be better off purchasing a legend for round £5 grand and even then how do you know it's all going to pan out?
Not that I've researched this in any way