I'd planned to start a walk today (9 Apr) from the free car park at Barber Booth (SK108847) only to find that it was closed for use by a BBC film crew making the second series of The Village. There are a few spaces under the nearby railway bridge but these were taken. I diverted to Edale only to find that half of this large car park was also occupied by BBC support trucks. I'm not sure how long this will last but if your heading that way it might be advisable to check with the Edale national park office.
Thanks for the report. I'll be in Castleton next week with my caravan and had already planned a similar route (the other way around) from Barber Booth and back down Chapel Gate. Slightly shorter but hopefully just as enjoyable.