I believe London is one of the places where USCIS has its International Office. That means you can get married in the UK, and file I-130 locally at the US consulate under the DCF processing. See below.
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Both methods are possible but I find the fiancé visa (K1) better because based on my experience, it is quicker and it is better to deal with the green card process while you are in the US. . However, timeframes can depend on backlog and personal circumstances, so I cannot predict a specific timeframe. Generally, fiancé visas are processed pretty quickly (2-6 months).
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That is correct in certain cases you may direct file the I-130 at the US consulate in London, which would be faster and easier, if you would be able to do so. For more info see http://london.usembassy.gov/dhs/uscis/i130filing.html.
Hugo Valverde's response to your question is general in nature, as not all the facts are known to him. You should retain an attorney experienced in immigration law to review all the facts in your case in order to receive advice specific to your case. Mr. Valverde's statement above does not create an attorney/client relationship and does not constitute legal advice.
It would likely be quicker for you to marry in the UK and proceed with an immigrant visa through DCF (direct consular filing).
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