  We present a new gravitational lens modelling technique designed to model
high-resolution interferometric observations with large numbers of visibilities
without the need to pre-average the data in time or frequency. We demonstrate
the accuracy of the method using validation tests on mock observations. Using
small data sets with $\sim 10^3$ visibilities, we first compare our approach
with the more traditional direct Fourier transform (DFT) implementation and
direct linear solver. Our tests indicate that our source inversion is
indistinguishable from that of the DFT. Our method also infers lens parameters
to within 1 to 2 per cent of both the ground truth and DFT, given sufficiently
high signal-to-noise ratio (SNR). When the SNR is as low as 5, both approaches
lead to errors of several tens of per cent in the lens parameters and a
severely disrupted source structure, indicating that this is related to the SNR
and choice of priors rather than the modelling technique itself. We then
analyze a large data set with $\sim 10^8$ visibilities and a SNR matching real
global Very Long Baseline Interferometry observations of the gravitational lens
system MG J0751+2716. The size of the data is such that it cannot be modelled
with traditional implementations. Using our novel technique, we find that we
can infer the lens parameters and the source brightness distribution,
respectively, with an RMS error of 0.25 and 0.97 per cent relative to the
ground truth.
