When we got setup on our overdraft at NatWest International (Off Shore), we had to provide credit references from the states first. Once received, we were granted £1000.00 and hope to never use it.
Regarding your Passport: I was told when we setup our overdraft that they wanted to know exactly when our UK Visa expired so they could end our line of credit 6 months prior to that date.
Why? If we did owe money, it gives us six months to pay it back before leaving the UK.
They stated if we become a resident or get another UK Visa, they would either extend or terminate the expiration date completely.
Best of Luck