Hey there Lois, There is a way round this problem, and you have mentioned it briefly but im not sure if you have considered this.
To get my first contract, I put the contract in my then girlfriends name and bank account, and then instantly swapped the contract over to my name and my bank account. This seemed to work well for me, but then I have never had bad credit as far as I know.
The point being that there are less checks when it is simply a change of bank account rather than initially opening the contract.
Although as you said, you do have bad credit history, and there are some check whenever you swap the account, so I cant vouch for whether you will be successful this way.
The other option obviously, is just to buy the phone outright (getting a refurbished phone you can get pretty good deals) and then just get a sim only contract or something similar to what you used to have.
Best of Luck!