And because of that, we don't have anything in her new name because no one would change it in the States (granted, we only tried her bank and the Social Security office).
My point was that you don't need to change anything in the US at all yet, because you don't live there at the moment, so there's no need to do it first.
So, just don't even think about the US stuff right now - you can sort that out later on - and instead I would first concentrate on changing her name in the UK... on things like her UK driving licence, council tax, electricity bills, phone bills, bank statements etc. You should just be able to contact the various companies you have accounts with and ask them to change her name on the account.
From what I can tell, as long as both her maiden name and your surname are listed on the marriage certificate, that is enough evidence of a name change for UK authorities.
So, you can also apply to change her name on her UK passport, by sending off your marriage certificate with the application.
And you can see about changing her name on her US passport... I found a link that said that as long as both your names are listed on the marriage certificate, it is sufficient evidence of a name change for a US passport, but it wasn't an official government link so that's not confirmed.
Once you have changed her name on her UK and US passports, you can start thinking about changing it on her SSN and other things in the US... because you will now have evidence of the new name.