Liam Payne took the top spot followed by his bandmates Harry Styles, Niall Horan, Louis Tomlinson and Zayn Malik.
The boy band also came ahead of Labour leader Ed Milliband on the PeerIndex list.
Musician Ed Sheeran came sixth, with PM David Cameron in seventh place.
All the members of 1D, except Zayn Malik, boast more than 12 million followers on the micro-blogging site, compared with just 400,000 for Cameron.
Family and friends of the teenage heartthrobs also dominated the top of the list with Louis' girlfriend Eleanor Calder being rated as more influential than Labour leader Milliband, who has just 200,000 followers, or Chancellor of the Execuquor George Osborne.
Mayor of London Boris Johnson limped in at 41, despite boasting 600,000 followers.
TV presenter Piers Morgan and London Times journalist and author Caitlin Moran claimed high spots just ahead of comedians Ricky Gervais and Stephen Fry.
PeerIndex analysed more than 10 billion tweets to compile the list of the 140 most influential individuals - chosen because posts on Twitter can only be comprised of 140 characters - which "provides a snapshot of national affinities."
Scores were not based on how many followers an individual attracted but on the amount of Twitter traffic they generated via other people responding to or re-tweeting them.
Stars of music, television and sport dominated the list with a scattering of journalists, bloggers and MPs.
Azeem Azhar, founder of PeerIndex, told the Daily Telegraph: "As Twitter has become more mainstream, the top 140 starts to resemble the contours of popular culture and power, the footballers, politicians and boybands.
PeerIndex top Twitter users top 10:
1. Liam Payne, @real_liam_payne, score 98, 12.3m, One Direction member, music
2. Harry Styles, @Harry_Styles, score 98, 15.4m, One Direction member, music
3. Niall Horan, @NiallOfficial, score 98, 13.4m, One Direction member, music
4. Louis Tomlinson, @Louis_Tomlinson, score 98, 12.2m, One Direction member, music
5. Zayn Malik, @zaynmalik, π score 97, 9.9m, One Direction member, music
6. Ed Sheeran, @edsheeran, π score 97, 7. 4m, singer-songwriter, music
7. David Cameron, @David_Cameron, score 97, 0.4m, Prime Minister, politics
8. Piers Morgan, @PiersMorgan, score 97, 3.6m, journalist and TV personality, journalism
9. Caitlin Moran, @caitlinmoran, score 96, 0.4m, feminist author and journalist, journalism
10. Ricky Gervais, @rickygervais, score 96, 4.9m, comedian and actor, entertainment