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→Xp. 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<log10ξ<−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 Δη, 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≈eBt 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.