Observations of sea-level change from localities around the British co
astline indicate that major spatial and temporal variations have occur
red over the past 15 000-10 000 yr. These observations provide a valua
ble data set for testing models of glacial rebound and for estimating
the Earth's response to surface loading as well as for placing broad c
onstraints on models of the ice sheet over the northern British Isles
in Late Devensian time. Simple models have been developed to examine t
he criteria required for a high-precision rebound model suitable for a
n inversion of the observations of sea-level change for earth- and ice
-model parameters. For such a model to have a precision of better than
1 m these requirements include: (1) introduction of the Fennoscandian
and more distant ice sheets into the model both as contributions to t
he sea-level rise and to the crustal deformation of the associated cha
nging ice and water loads; (2) an expansion of the ice and meltwater l
oads to very high spherical harmonic degree including terms up to abou
t 240 for the water-load term; (3) the development of higher iteration
solutions of the sea-level equation in order to model accurately the
meltwater load contribution to sea-level change; (4) the introduction
of loading cycles before the attainment of the last glacial maximum fo
r both the British ice sheet and the other major but more distant ice
sheets; and (5) the introduction of time-dependent coastlines during t
he period of rapid global sea-level rise. The sea-level predictions ar
e strongly dependent on both earth-model and ice-model parameters but
because observations are available from a wide range of locations with
in and beyond the former ice-sheet margins, some separation of the two
types of parameters is possible. For example, the models exclude the
possibility that a substantial ice load occurred over the North Sea be
tween Scotland and Norway in Late Devensian time and that the maximum
ice thickness over northern Great Britain is unlikely to have exceeded
about 1500 m during the last glacial maximum. The earth model paramet
ers that can be resolved are the lithospheric thickness and the upper
mantle viscosity. A high resolution model incorporating the above mode
l criteria and used to infer ice-and earth-model parameters from the o
bservations of sea-level change is developed in the accompanying paper
.