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plxarc
PhilPub
Just a small contribution from me, but I would probably avoid riding up Westerham Hill. It's a fairly busy road and not much fun having cars overtaking frequently along a narrow carriageway when you're struggling up a 12% gradient. Any of the hills just to the East would be more pleasant, if just as steep: Hogtrough, Brasted and Sundridge Hill, or Star Hill a little further over.
If it was me I'd either go up Brasted or Sundridge Hill, then through Knockholt and along Grays Lane before picking up the route again towards Biggin Hill. Or if you still wanted to go along that section of the Pilgrim's Way (and it's a very nice hedge-lined country lane) take a small detour involving the A25 through Brasted itself, come along the Pilgrims Way in the other direction.