Can we start with what makes an American roller coaster?
It certainly can't be something made by a European firm, which rules out B&M, Intamin, or Schwarzkopf.
It could also have to be something older. The golden age for American roller coasters was the 1900 to 1930s, followed by the second golden age that started in 1972 and has run until present.
I propose two roller coaster models as the "classic" American roller coaster.
The wooden out-and-back roller coaster. It was a concept pioneered by John C. Allen, the famous American designer who worked for Philadelphia Toboggan Company during its hay day and is credited with patents of many common roller coaster technologies. Allen also helped spark the second golden age of roller coasters with his help in the construction of the Racer at Kings Island. A seemingly all-American design, and a staple attraction at many American amusement parks.
A splinter off of this design would also be the twister design. Afterall, the Coney Island Cyclone and Giant Dipper at Belmont Park (arguably two of the most famous wooden coasters in the world) are twister designs.
The Arrow multi-loop roller coaster. Arrow Dynamics was the firm roller coaster manufacturer to break into the modern steel roller coaster market with the construction of the Matterhorn Bobsleds at Disneyland. Arrow also quickly entered the inversion game, building the first modern inverting steel coaster in 1975 (Corkscrew at Knott's Berry Farm). This roller coaster officially held the record for most inversions in the world. The following year, Intamin built the first modern loop with Revolution at SFMM, but Arrow opened Corkscrew at Cedar Point six days later with three inversions, continuing the record claim for most inversions. Arrow continued to maintain the record for most inversions through to Viper at SFMM with 7 inversions, opened in 1990. Intamin eventually claimed the title for most inversions in 1998 with the opening of Volcano, The Blast Coaster; 23 years after the opening of Corkscrew at Knott's Berry Farm.
So all of this being said, it is difficult to find older-style inverting steel coasters or wooden coaster in the UK. But of what can be found, The Big One or Revolution at BPPB would arguably be the most "American." Both were built by Arrow Dynamics, and capture much of what had been established in the U.S.