Hi Sheala
From London, GNER trains run to York. change at York for Scarborough & then a bus from Scarborough to Whitby. Trains from York to Scarborough run every hour & buses from Scarborough to Whitby run every hour too.
This souds onerous but I live in Whitby & regularly have to go down to london & it's really not too bad. Would suggest that you bookthe London to York train seat but otherwise no need to book.
Have to report that the sun is shining in lovely Whitby!