If you stick with your current provider, all they will do is just check to make sure that your payments are up to date and you will be able to upgrade with no problem.
I've followed the links on the website and it only takes you to the websites of the mobile phone companies. Personally I think it would be very unlikely for someone to get a contract with a new provider whilst they are BR (there's a difference between having bad credit history and being BR), but if anyone could prove me wrong that would be great!
Tomorrow is a mystery, yesterday is history, today is the present, a gift to make the most of.