Hi.
I have just filed my request with the USCIS in London. The first thing you need to do is figure out whether you meet the requirements for DCFing (direct consular filing) or if you have to file with a service center. The former way of filing happens directly with USCIS London which is at the embassy and takes about 4-5 months from filing till you have visa in hand assuming nothing goes wrong. With the latter, you have to file from here but with a US service center and the whole process can take up to a year or so. To DCF you have to have lived in the UK for at least 6 months and have proof that the UK is your main home (you can find more info on the US Embassy in London's website).
So, you send off your I-130 first then you get a notice saying the I-130 has been approved and you get sent a pack for the visa petitioner (the UK citizen in this case). Your spouse fills those out and sends them in once they have gathered all the documents requested. Once that is done, you wait for an interview date. In the meantime, the visa petitioner has to undergo a medical examination that would ideally be ready with results by the time the interview comes around. On the interview itself, if you have all the documents they need and nothing is out of order, they should tell you whether the visa has been approved or not. If it has, all you do is wait for that passport to come in the mail with a visa stamped on it along with a brown envelope full of documents. Once you have this, you are ready to enter the US.
After arrival in the US, you apply for a social security card/number and wait for the actual residency card (green card) to arrive in the mail. Voila!
June