Thanks for your question.
As a foreign national resident in this country with leave to remain in this country you will have to apply (for you) for a certificate of approval in order to get married here. You will note be able to get married here without one. Info here:-
You will have to apply using form COA. This and the guidance notes for the form explaining how to complete it are on the right hand side of the above link. The COA will be valid for a period of 6 months from the date of the grant. You will have to get married during this time.
You fiance will have to apply to the British Embassy nearest to her for a Marriage Visitor's Visa. This, again, will be granted for a period of 6 month and you will have to marry during this time. She will have to submit evidence that you are to marry (eg. statements made by both of you, correspondence in which you confirm in which is is obvious that you are to marry and possibly evidence of booking somewhere where you are to marry and have the ceremony.
She will need to apply using form VAF1F which is available on this page. Scan down to a little over halfway down the page to Special visitors: Visitors coming to get married on the below link:-
It is important that you submit both applications at the same time, as obviously you are both time limited by 6 months on each visa.
Once you both have these visas you, as foreign national, can get married.
You will receive a Marriage Certificate which is evidence of your marriage and is accepted as such in the United States. You can obtain certified copies of your marriage certificate at any time from the registry office for the district in which you marry.
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