  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 $\chi_{SWT}=0.0794$.
