HSBC are well known for making it sound as if you have to have everything with them before they'll consider helping you with an account or borrowing, though they'll never say you HAVE to move from Natwest as they're not allowed (Financial Services rules).
If you would like to move your account to HSBC (who aren;t that bad as long as you just use their current account and borrow money / take insurance elsewhere) then they'll usually agree a similar overdraft to Natwest so you can write a cheque to Natwest from your new HSBC account to clear the overdraft. This will put you straight into your new overdraft but as long as it's agreed it's not a problem.
Hope this helps!