Anubeon: I cancelled my Halifax All in One card about two months ago, having opened the account in my first year as a postgraduate student. Yet earlier today I was informed that as a postgraduate student I was not eligible for the Halifax All in One card,
I take it you had a particular reason for cancelling your previous card? Did you have a Plan B?
Many issuers won't reissiue a card until some time has elapsed, which may be the real reason and nothing to do with being a postgraduate student. Perhaps they know you are a student because you have a student current account?
If you haven't had too many recent applications you can probably afford to try elsewhere. Use the credit card search on this website, taking care to select "Purchases" and checking both the Sponsored and the Full results. If you are unsuccessful I guess that is lesson learned and you might need to rely on a Halifax student credit card.
Regarding your status when making an application, be careful about selecting "student" if actually you are a "postgraduate student" with a stipend and there is a better description.