Try Halifax..
i dont know if they have in Glasgo, but they are very easy to open new accounts, if im not wrong you can even do it online.. but if you still want HSBC i can give you an email of a lovely manager in HSBC in Belfast, not that it metter, i think all the same, and i used to work with her all the time and maybe she can help you, ussualy she arrange all paper work and just letting your branch know you are coming to sign the papers..