It's not so bad, actually; you have to file FBAR, which will take you a couple of hours, but that's about it.

Actually some Uk /Euro banks wont take American customers to avoid the extra costs the IRS insists on.

You actually mean no -- Estonia making it easier is exceptional, and only happened in June.

For example, I considered opening this Tesco account, since I need to keep about £1500 in my British account for student loan payments. Tesco offer 3% interest on the balance, but I should have opened the account before I emigrated.

Yeah, my accounts in the US always get flagged for manual review at creation time and "extended initial funds holding" because my SSN doesn't match my DOB (because it was issued when I got my Green Card, and not when I was born).

I've even had to convince banks that they're allowed to open an account for me in the first place...

Right, I'm in the EU and and EU citizen to boot, so that's probably why it's been easier for me. Funnily enough, the UK has been the most difficult country to open a bank account in, because of their insisting on using utility bills as proof of residence, and apparently a residence is more or less a must. My first UK account took a few days of hassling to get set up, because I didn't yet have a residence, but was living in a hotel. A proof of employment and a couple of face to face meetings with supervisors cleared that up though.