We apply the coupled cluster method (CCM) in order to study the ground-state properties of the (unfrustrated) square-lattice and (frustrated) triangular-lattice spin-half Heisenberg antiferromagnets in the presence of external magnetic fields. Here we determine and solve the basic CCM equations by using the localised approximation scheme commonly referred to as the `LSUB\(m\)' approximation scheme and we carry out high-order calculations by using intensive computational methods. We calculate the ground-state energy, the uniform susceptibility, the total (lattice) magnetisation and the local (sublattice) magnetisations as a function of the magnetic field strength. Our results for the lattice magnetisation of the square-lattice case compare well to those results of QMC for all values of the applied external magnetic field. We find a value for magnetic susceptibility of \(\chi=0.070\) for the square-lattice antiferromagnet, which is also in agreement with the results of other approximate methods (e.g., \(\chi=0.0669\) via QMC). Our estimate for the range of the extent of the (\(M/M_s=\))\(\frac 13\) magnetisation plateau for the triangular-lattice antiferromagnet is \(1.37< \lambda < 2.15\), which is in good agreement with results of spin-wave theory (\(1.248 < \lambda < 2.145\)) and exact diagonalisations (\(1.38 < \lambda < 2.16\)). The CCM value for the in-plane magnetic susceptibility per site is \(\chi=0.065\), which is below the result of the spin-wave theory (evaluated to order 1/S) of \(\chi_{SWT}=0.0794\).