It is illegal in the United States to marry a green-card holder.
In order to marry, a greencard applicant must provide information about his or her background and meet the following criteria: be at least 18 years old and a citizen of the United State at the time of application; be unmarried at the date of application or application for admission to the United Kingdom; and be at a level of economic capability to support themselves and their children.
The Green Card Application form can be found here.
The U.S. Embassy in London advises that green-carpet weddings are not recommended as they may require additional travel and security requirements, but that they are still legal.
“The Green Card has been considered a necessary document of entry to the U.K., and the U,K.
Embassy strongly recommends applicants to apply for and obtain a green Card within their own country of residence,” it said.
“In the U., green card holders can apply for a UK passport upon arrival in the U.”