A dedicated sample of Large Hadron Collider proton-proton collision data at centre-of-mass energy √s = 8 TeV is used to study inclusive single diffractive dissociation, pp → X p. The intact final-state proton is reconstructed in the ATLAS ALFA forward spectrometer, while charged particles from the dissociated system X are measured in the central detector components. The fiducial range of the measurement is −4.0 < log10 ξ < −1.6 and 0.016 < |t| < 0.43 GeV2, where ξ is the proton fractional energy loss and t is the squared four-momentum transfer. The total cross section integrated across the fiducial range is 1.59 ± 0.13 mb. Cross sections are also measured differentially as functions of ξ, t, and ∆η, a variable that characterises the rapidity gap separating the proton and the system X. The data are consistent with an exponential t dependence, dσ/dt ∝ e Bt with slope parameter B = 7.65 ± 0.34 GeV −2. Interpreted in the framework of triple Regge phenomenology, the ξ dependence leads to a pomeron intercept of α(0) = 1.07 ± 0.09.