They burst on to the British music scene in 2005 when their single “I Bet You Look Good on the Dancefloor” went straight in at number one. Now, the “unstoppable” Arctic Monkeys have made history as the only independent group whose first five albums have gone to the top of the charts.

Their achievement eclipses that of Britpop superstars Blur, who also had five consecutive No 1 albums but whose run started with 1994’s Parklife, their third record, and ended with them no longer being signed to an indie label.

Erasure had four but their success also began with their third studio release, 1988’s The Innocents, and the last was a greatest hits collection. The Prodigy can match that sequence, but their first, 1992’s The Prodigy Experience, failed to crack the top 10.

Their closest challengers are probably Stereophonics, who can also boast five consecutive No 1 albums, but their run started in 1999 with their second release, Performance and Cocktails.

Martin Talbot, chief executive of the Official Charts Company called Arctic Monkeys’ run an “exceptional achievement”, while praise for the album itself has been equally effusive.

NME editor Mike Williams called AM “absolutely and unarguably the most incredible album of their career, [and] it might also be the greatest record of the last decade.” He added:

“It’s not, however, the work of a band operating at their absolute peak – that’s yet to come. It’s the work of a band still growing.”

A spokesman for the Official Charts Company said yesterday: “It’s proof that you don’t have to be backed by a multinational to be successful. I guess it’s kind of the flip-side to the likes of the X Factor and The Voice.”

It has been a good week for the band, who were nominated for the Mercury Prize on Tuesday, an award they won in 2006 with Whatever People Say I Am, That’s What I’m Not. AM is also now the second-fastest selling album of the year behind Daft Punk’s Random Access Memories, which sold 165,000 copies in its first week of sale back in May.

The Official Chart classes an independent band as one signed to a label not backed by one of the three major music labels: Universal Music Group, Sony Music Entertainment and Warner Music Group.

Arctic Monkeys still have a way to go to catch the ultimate chart-toppers, The Beatles, whose first eight records – from Please Please Me in 1963 to Sgt Pepper’s Lonely Hearts Club Band in 1968 – hit the top spot.

But if Mike Williams is right, who’s to say they won’t?

Forged in Steel City: Arctic Monkeys timeline

In 2003, Arctic Monkeys played their first gig in the Grapes, a pub in Sheffield, a year after the band was formed by four school friends. They knew each other from the age of seven, growing up in High Green, a suburb of Sheffield.

The band gave away demo CDs and fans put them on MySpace bringing attention to their music. Their debut album in 2006 Whatever People Say I Am, That’s What I’m Not contained the hit single “I Bet You Look Good On The Dancefloor” and became, at the time, the fastest-selling debut album in British history.

They released albums Favourite Worst Nightmare in 2007, Humbug two years later and Suck It and See two years after that. In 2012 the band played at the Opening Ceremony for the Olympic Games and this year headlined the Pyramid Stage at Glastonbury.

The members of the band, which has won five Brit Awards and a Mercury Prize best album award, now live close to each other in California, where the latest album AM was recorded. AM debuted at No 1 in the charts, their fifth consecutive album to do so.