In early 1993, Radiohead began to attract listeners elsewhere. "Creep" had been played very frequently on Israeli radio by influential DJ Yoav Kutner, and in March, after the song became a hit in that country, Radiohead were invited to Tel Aviv for their first live gig overseas. Around the same time, the San Francisco alternative radio station KITS added "Creep" to its playlist. Soon other radio stations along the west coast of the United States followed suit. By the time Radiohead began their first North American tour in June 1993, the music video for "Creep" was in heavy rotation on MTV. The song rose to number two on the US modern rock chart, entered the lower reaches of the top 40 pop chart, and hit number seven in the UK Singles Chart when EMI rereleased it in the UK in September.

Unexpected attention for the single in America prompted EMI to improvise new promotional plans, and the band shuttled back and forth between continents, playing over 150 concerts in 1993. Radiohead nearly broke up due to the pressure of sudden success as the Pablo Honey supporting tour extended into its second year. The band members described the tour as difficult to adjust to, saying that towards its end they were "still playing the same songs that recorded two years previously ... like being held in a time warp," when they were eager to work on new songs.

Radiohead began work on their second album in 1994, hiring veteran Abbey Road Studios producer John Leckie. Tensions were high, with mounting expectations to deliver a follow-up to match the success of "Creep". Recording felt unnatural in the studio, with the band having over-rehearsed the material. Seeking a change of scenery, they toured the Far East, Australasia and Mexico and found greater confidence performing their new music live. However, troubled by the fame he had achieved, Yorke became disillusioned at being "at the sharp end of the sexy, sassy, MTV eye-candy lifestyle" he felt he was helping to sell to the world.

My Iron Lung, an EP and single released late in 1994, was Radiohead's reaction, marking a transition towards the greater depth they aimed for on their second album. Promoted through alternative radio stations, the hard-edged single's sales were better than expected, and suggested for the first time that the band had found a loyal fan base beyond one hit. Having introduced more new songs on tour, Radiohead finished recording their second album by year's end, and they released The Bends in March 1995. The album was driven by dense riffs and ethereal atmospheres from the band's three guitarists, with greater use of keyboards than their debut. It also received stronger reviews for both songwriting and performances.

While Radiohead were seen as outsiders to the Britpop scene that dominated the media's attention at the time, they were finally successful in their home country with The Bends, as singles "Fake Plastic Trees", "High and Dry", "Just", and "Street Spirit (Fade Out)" made their way to UK chart success; the latter song placed Radiohead in the top five for the first time. In 1995, Radiohead again toured North America and Europe, this time in support of R.E.M., one of their formative influences and at the time one of the biggest rock bands in the world. The buzz generated by such famous fans as Michael Stipe, along with distinctive music videos for "Just" and "Street Spirit", helped to sustain Radiohead's popularity outside the UK.

However, Radiohead's growing fan base was insufficient for them to repeat the commercial popularity of "Creep" worldwide. "High and Dry" became a modest hit, but The Bends peaked at 88 on the US album charts, which remains Radiohead's lowest showing there. Radiohead were satisfied with the album's reception. Jonny Greenwood said, "I think the turning point for us came about nine or twelve months after The Bends was released and it started appearing in people's polls for the end of the year. That's when it started to feel like we made the right choice about being a band".