you could try these guys... http://www.gttowing.co.uk/
they used to hire out a landrover 90 or 110 for towing.
probably won't deliver to Gatwick, but it's not such a difficult train journey from south london to just outside north london
Problem is that they may not offer insurance at all - last time I tried to hire from SHB they said - you have to use your own - that was about 3 yrs ago!!!