Does anyone know the best way to get from Robin Hood's Bay to London?
Go to www.traveline.info and it will tell you.
Bus X93 to Scarborough - then local train to York (pay on the day). Then express train to London (Kings Cross). Takes just over 4 hours but you would probably want top stop off in York. Best to advance book the York > KGX train to get a cheaper price.
Train schedules & fares for different dates (as of now) at www.nationalrail.co.uk