I moved from Ireland to the UK - both ~are~ were members of the EU, and there was no visa requirement to move. The only thing I had to do when I got here was get a bank account and a national insurance number (think SSN) for tax calculations. I tried 6 high street banks (RBS, TSB, Santander, Barclays, Halifax and Nationwide) who would not give me a bank account without a utility bill for proof of address, and would not accept my tenancy agreement, however I couldn't get a utility bill without a direct debit. In the end, someone told me HSBC would give me a "passport" account, and I used that to bootstrap the rest of the process. It was an absolutely infuriating process full of "computer says no", and absolutely nobody willing to help.
I had a similar experience, and I had a passport to prove my UK citizenship. It's a giant knot where everything relies on something else and you need to keep at it until one thing let's you in. It felt impossible and I feel like I had the best case scenario; I can't imagine how people without a support network can do it.
