If you still live in the UK, you are better off doing the process through the Consulate. It is cheaper, it is quite fast and (lastly), moving here and then filing could be viewed as visa fraud.
If any children were born during the marriage and the US Citizen was already a Citizen at the time of their birth, then the children are most likely US Citizens. If that is the case, contact American Citizen Services at the Embassy to get the children Report of Certificate of Birth Abroad.
As for your spouse, the process involves the US Citizen filing an I-130 with USCIS. If the I-130 has a foreign address for the petitioner, USCIS will process it in 1-2 weeks and forward the case to the National Visa Center, where the fee of $318 (filing for adjustment of status in the U.S. costs $1,070) will be paid and paperwork will be submitted. Upon review of the documents, an appointment will be scheduled for the Consulate. The whole process, if you stay on top of it, can be completed in 3-4 months.
Answered on Jul 30th, 2012 at 10:58 AM