The Beatles. The Rolling Stones. Radiohead. 5ive. The list of British all-male bands to have taken the American music industry by storm is almost endless.

Now, the name One Direction can be added to the canon. The band – made up of five not unattractive young men, each with their own carefully crafted personality and dress sense – are managed by music mogul Simon Cowell, and are in the US trying to make it big.

The band were spawned by the British version of The X Factor, Cowell's show that proved more successful in the UK in a genre where American Idol – created by the other British pop mogul called Simon: Fuller – continues to dominate in the US.

As individuals, the band members failed to reach X Factor's final stages, but were put together – after a suggestion by guest judge Nicole Scherzinger – to compete as a group. Under Cowell's expert mentorship, they crashed out of the 2010 series in third place.

Undaunted by the public rejection of his protégés, Cowell signed them up anyway. Two wrongs might not make a right, but who said anything about five?

Their debut album, Up All Night, reached No 2 in the UK charts. It's being released in the US on Tuesday, and the first big stop on the US publicity tour was an appearance on NBC's Today show on Monday morning. The band took over Rockefeller Plaza, packed with the obligatory screaming tweens, to perform three catchy tracks from the album. They opened with You Don't Know You're Beautiful, which reached No 1 in Britain, followed by One Thing and More Than This.

Even by pop-puffery standards, the pre-performance interview, with presenters Ann Curry and Matt Lauer, was probably not the most taxing they have endured. Asked by Curry about the best and worst moments of sudden fame, Zayn Malik said: "Since we got put together, we've made four best friends, you know, we've lived together, we're on the road and we do something that we love every single day, so for us that's the most amazing part."

"The only downside is we don't see our friends and family as much as we'd like to but other than that, you know, we're just enjoying everything that, you know, life is throwing at us at the minute, so."

The band have proved popular with US audiences while supporting Big Time Rush, and are scheduled to appear on Saturday Night Live next month as they push into the American market. A collaboration with fellow musician Justin Bieber could even be on the cards, with Bieber's manager Scooter Braun tweeting that the Canadian "thinks [One Direction] are good dudes".

• Read an exclusive interview with One Direction on Thursday at guardian.co.uk/music