Back dated EDP

I have been waiting on word back from DWP about back pay and to ask them to transfer me on to Income Related instead of Contribution ESA which I've been on for 10 years. Its been a couple of months and I heard it takes around 12 weeks to get a response but can't they put me on the IR ESA in the meantime while they decide if I'm entitled to back pay?
I'm currently looking to move out of my apartment where I'm being intimidated so any back pay would pay for a new place. If I ring do you think they might at least admit that I'm on the wrong ESA & will receive the BP so I could borrow on the strength of that? Or will they not be permitted to tell me that at least?
Many thanks.