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, $pp\to Xp$. 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 and , where $\xi$ is the proton fractional energy loss and $t$ is the squared four-momentum transfer. The total cross section integrated across the fiducial range is $1.59\pm 0.13 mb$. Cross sections are also measured differentially as functions of $\xi$, $t$, and $\Delta \eta$, a variable that characterises the rapidity gap separating the proton and the system $X$. The data are consistent with an exponential $t$ dependence, $d\sigma /dt\propto eBt$ with slope parameter $B=7.65\pm 0.34 GeV-2$. Interpreted in the framework of triple Regge phenomenology, the $\xi$ dependence leads to a pomeron intercept of $\alpha (0)=1.07\pm 0.09$.