Help! Bluehost has deactivated my account

Help!

I've helped set up 3 separate hosting accounts for clients through Bluehost? and in all their wisdom they've decided to cancel them for 'verification issues'. I've set up other accounts before and this is the first time it's happened. Unfortunately being in Australia the time delay means they can't do anything to effectively our Monday evening, which is too late. I need to urgently look for another hosting provider, so any recommendations would be appreciated.

I also don't want to lose all the work I've put in on those sites though so what recommendations on steps to take to transfer my files from one host to another?