Susan/DickDo you want to stay in Herts. both Saturday and Sunday nights (12/13)? I'll sort out with Kevin/Alan if you can confirm.
Afraid Gatwick is almost the worst possible place for train connections. Somebody may well be able to drive you round the M25 though.
We're more or less on the Kings Cross line (to North East England and Scotland) and also close to the main London North East road (the A1), one of which you'll need to take to get to Whitby. You could always put up for the night with us on the way up or down (welcome) and we could arrange transport. Towersey isn't very far away either. London 30-45 mins by train. You could use us as a fallback failing other transport/accommodation arrangements.
Cheers!
IanC