The NFL first gained popularity in Britain in the 1980s when broadcaster Channel 4 began showing games.
The Super Bowl was screened live for the first time in January 1983, featuring the Dolphins and the Washington Redskins, and a series of pre-season games were played at Wembley in the late 1980s and early 1990s.
The Dolphins remain one of the most popular teams in Britain, trailing only the New England Patriots, according to the 125,000 registered users of the NFL's British website http://www.nfluk.com.
"For a short period the Super Bowl outrated (soccer highlights show) Match of the Day but then other sports started doing better, re-inventing themselves," Kirkwood said.
English football launched its hugely successful Premier League in 1992 while more recently cricket has found a new format, Twenty20, which has helped the game reach a wider audience.
The NFL in the last three or four years has, however, begun to gain wider coverage and there will be 130 live games on television in Britain this year, more than the Premier League, Kirkwood said.
The BBC is showing highlights of the Wembley game and live coverage of the Super Bowl.
Kirkwood said one of the keys for the sport to be successful in the country was to develop local talent. The league will soon sign off on a five-year plan to develop British players.
"We will then have a clear pathway for British players to play in NFL games," he said.
Two British-born players will be in the Giants team at Wembley, kicker Lawrence Tynes from Greenock in Scotland and Londoner Osi Umenyiora who is a defensive end.
The Wembley game was quickly sold out with 87 percent of the fans coming from Britain and the balance evenly split between mainland Europe and the United States.
The Giants will be hosted by in London by Premier League football club Chelsea while the Dolphins will be using the facilities of one of the country's leading rugby union teams, London Wasps.
The struggling Dolphins, who have lost all seven of their games this season, will be without running back Ronnie Brown and safety Renaldo Hill.
They suffered torn cruciate ligaments during the 49-28 loss to the New England Patriots on Sunday and are out for the season.