you should have no problem . have your prior year tax forms , W2's and letter from your employer etc . 10 years ago when i bought my first house ACC bank was the only instution(that i was aware of) that would give a loan to a non resident, in addition it allowed me to open a US Dollar account and it was very handy as i waited until the exchange rates were in my favour to convert to punts .
i still have the mortgage with ACC bank but i am moving back in september and will look in to getting a better rate .
good luck with it