Having been turned down on-line by EE for phone, tv and unlimited broadband, I drove down to the nearest EE shop and got accepted for the whole Sheebang for £28.50/month.
I think that the call centres are all trained to tick boxes and not use their brains too much. I got turned down for a credit card because I had no debt and no mortgage - how stupid is that?
I hope that you get it all set up without problem.