They changed the requirements just after I actually got mine done, so I know they're asking for way more paperwork than they even asked from me when they sent me away the first time...
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Both names on the lease? That will be good - and if you can get maybe separate letters addressed to each of you from the landlord about the council tax being included and the fact that you have a coin fed meter on the premises - it will be something from this year showing that you two are residing at the same place.
Look through ALL your old paper work.
They didn't seem to want the bank accounts to show funds - they wanted them to show proof of living at the same place, so I'd take the balanceless printed statements you're still receiving from your old bank.
Credit card bills, "solicitation" post that may actually have your names on it, pay stubs if they show your address...
The problem we had was that the form was the old one, asking for proof for the past year or so, and because FLR is 2 years now they insisted on 2 years of proof, even though the form didn't and NOWHERE on the website (at the time) did either. I think it was a bit cheeky of them to actually send me away based on requirements that I couldn't possibly have known about - but at least we didn't get charged twice like someone else I heard about.

What exactly do you have for the past two years? (You can PM if you feel it's too "personal"!)