The production of single top quarks and top antiquarks via the t-channel exchange of a virtual W boson is measured in proton-proton collisions at a centre-of-mass energy of 13 TeV at the LHC using 140 fb−1 of ATLAS data. The total cross-sections are determined to be σtq=137−8+8 pb and σt¯q=84−5+6 pb for top-quark and top-antiquark production, respectively. The combined cross-section is found to be σtq+t¯q=221−13+13 pb and the cross-section ratio is Rt=σtq/σt¯q=1.636−0.034+0.036. The predictions at next-to-next-to-leading-order in quantum chromodynamics are in good agreement with these measurements. The predicted value of Rt using different sets of parton distribution functions is compared with the measured value, demonstrating the potential to further constrain the functions when using this result in global fits. The measured cross-sections are interpreted in an effective field theory approach, setting limits at the 95% confidence level on the strength of a four-quark operator and an operator coupling the third quark generation to the Higgs boson doublet: −0.37<CQq3,1/Λ2<0.06 and −0.87<CϕQ3/Λ2<1.42. The constraint |Vtb| > 0.95 at the 95% confidence level is derived from the measured value of σtq+t¯q, assuming that the Wtb interaction is a left-handed weak coupling and that |Vtb| ≫ |Vtd|, |Vts|. In a more general approach, pairs of CKM matrix elements involving top quarks are simultaneously constrained, leading to confidence contours in the corresponding two-dimensional parameter spaces.