My first day on the job, I walked over to a Natwest branch and got the following through setting up the salary direct deposit.
1) a checking account
2) a savings account
3) a credit card with an initial limit of, I think, 500, long since raised to more than I'd want;
4) a debit card with a hologram that verifies personal checks up to 100 and also functions as my ATM card
I basically remember the bank giving me these last two, since it's not my habit to be looking for credit cards and at the time I'd never seen/used a debit card. All that I'd wanted was an ATM card that could transfer money between my checkings and savings. While I got an ATM card, Natwest can't figure out how to let you transfer money between two kinds of accounts, go figure.
The big four banks do differ in their policies, so it's not a waste of time to shop around. If Lloyd's gives you a hassle, then drop them. I mean loyalty to global capitalism is about the last thing we need to internalize!