The process was far less daunting than I expected.
My main recommendation is ensure all your paperwork is in order and that you have a copy of everything you need on you! Emphasis on the police record, partners Tax returns/affadavit. Make sure all of this is with you.
I did feel nervous because it is such an important occassion. At window one, you have your documents taken and checked, and fingerprints taken. At window two you go through some questions about the relationship (My questions were: when did you marry? what does your partner do? how long did you live together in London? how long has your partner been back in the USA?)
The staff are very nice, they're very straightforward and helpful.