I was with HSBC for about 7 years and got a good overdraft limit during uni (I think it was £1.5k at year 4). I left them a year after uni because they cheapened out when I wanted a larger overdraft/credit limit, applied for a mortgage and business bank account. Bear in mind that I am their ideal type of customer (always pays bills on time, pays a good amount in interest rates, low debt/earnings ratio).
I work, make real money and it seems that Lloyds TSB rewards me for that. HSBC declined my mortgage application rather quickly whereas Lloyds approved it despite being a fairly new customer. I got £10k credit limit on the business credit card (as opposed to £5k from HSBC) when I started my business, and the credit limit on my personal credit card is twice of what HSBC offered (same interest rate though). I felt that lloyds trusted me more even as a new customer, while HSBC had a low level of trust despite being with them since I was 16!
The banking system of lloyds is also much better, and the HSBC one seems to only have been improved aesthetically.
I had a business bank account for a month with HSBC and the difference between the personal and business banking customer service (usually at different floor in the branch) would surprise you. With lloyds I get the same customer service as a personal customer that I would get as a business customer with HSBC.
HSBC isn't terrible, but Lloyds TSB would be the best in my opinion.