We took the train from London to Carlsie then a train to St. Bees. Train from London took 6 or 7 hours departing london morining and arriving St. Bees late afternoon. On the return from Robin Hood's Bay, local bus to Whitby then train back to London. We had booked the walk through Contours Walking Holidays and they provided detailed recommendations on getting to and from the start/finish.
https://www.contours.co.uk/coast-to-coast-walk
Travel Information Detailed instructions on how to get to the start of
the holiday and back from the end, are sent to you upon booking. A
summary is given below:
By Air - The most convenient major city and international airports are
Manchester, Glasgow and Leeds.
By Rail - There is a rail station at the start of the trail (St Bees).
The nearest rail stations to Robin Hood?s Bay are either Whitby (about
6 miles away) or Scarborough (about 20 miles away).
By Bus - Various buses run to St Bees and from Robin Hood's Bay.
From London - Trains run from London Euston to St Bees.
Return To The Start - The easiest way to return to the start of the
trail is to take a bus/taxi from Robin Hood's Bay to Scarborough rail
station. From there trains run to St Bees.
It is very easy to travel to the start (and return home from the end)
of the holiday using public transport. Please click here for more
information.
Added note: We arrived a couple of days early in London to adapt to time change by walking about in London for a couple of days before taking the train to St. Bees. Arriving early also gave us a cushion in the even that our checked bag was delayed. Contours transfered one bag each allowing us to walk with only the day's essentials.