Recorded with producer Roy Carter, formerly of Heatwave, the album features a distinctly English style of synth-funk similarly to contemporaries Hi-Tension and Light of the World.

"[4] "Don't Tell Me", which was issued as the follow-up single, is funkier in comparison,[7] while the title track is a "jazzily bounding" instrumental that interlays guitar, bass and keyboards and which increases its tempo after an 118bpm intro.

"[10] In a contemporary review for Smash Hits, Beverly Hillier described Central Line as being "amongst the forerunners of British dance music" and hoped the album would "help put them where they belong," highlighting the title track for being "the kind of brilliant instrumental that will become a dancefloor sensation.

"[7] A reviewer for Aberdeen Evening Express, who had previously enjoyed "Walking Into Sunshine", praised the album and hailed Central Line for being "[f]our young Londoners showing the Americans how to play first class funk.

He nonetheless felt that, despite being "full of infectious choruses and catchy dance tunes," the album failed to do the group justice, writing: "Central Line are mid Atlantic, with an Anglo-American appeal that's frankly neither here or there.

"[25] In 2007, The Guardian included Breaking Point in their list of "1000 Albums to Hear Before You Die," with the caption: "Central Line, like their Brit-soul compatriots Hi-Tension and Light of the World, were trying to make slick synth-funk in the vein of Herbie Hancock or Quincy Jones, but anthems such as 'Walking Into Sunshine' constantly betray their Englishness, with a pleasingly punky, clunky brand of funk and a raw dub sensibility.

"[5] In 2014, the newspaper included "Walking Into Sunshine" in its list "Britfunk: 10 of the best", with contributor Lester calling it "a new high in terms of a British version of American post-disco slickness" and highlighting its "sonic immaculacy and gorgeous escapist yearning.

"[6] In a review for Uncut of Central Line's The Collection (2003), Marcello Carlin said that "Walking Into Sunshine" earned the band "immortality" and wrote that the compilation made "noticeable how much better" the material from Breaking Point was to the group's later work, describing "That's No Way to Treat My Love" and "Don't Tell Me" as "US funk-rivalling highlights.