The distribution of the publication coincides with the physical release of the band's eighth studio album The King of Limbs.
The newspaper is available at select locations globally, with the London supply being distributed from Dray Walk in Shoreditch. Frontman Thom Yorke is believed to be handing out copies personally.
A video posted by XL Recordings on Twitter shows a queue of hundreds of people that stretches around the block.
The paper is also available outside the Bread and Butter Cafe, Tibs Street, Northern Quarter, Manchester and on Dundas Street, Glasgow.
The band announced the release of the newspaper on Friday. They are also going to release a 'newspaper edition' of the album on May 9.