This story first seems to have appeared in a book called Tales of the Fens, by William Barrett, published in 1963. The story had been told to Barrett in 1900, by a fenman called Chafer Legge, who was a bare fist fighter and fen skater.
Wherever the story has appeared since then, it seems to have been based on this account.
A witches' coven
Grey goose feather
There is one other intriguing reference which may be relevant, however. A prominent member of a witches’ coven at Brickett Wood, in Hertfordshire, in the 1960s, had previously been a member of a coven in Norfolk. This coven uses a grey goose feather as a symbol and for passing messages. This man claimed that the coven had been meeting together in unbroken succession since Anglo-Saxon times.
Charles I by Sir Anthony van Dyck
The story does of course have some other factual basis, in that Charles I really did pass this way whilst fleeing from his enemies. In the last stages of the English Civil War, he had made his headquarters in Oxford. By April 1646, the Parliamentary armies were closing in on him there, and the decision was made by Charles and his advisors that he should escape and try and make his way to the Scots army in the north.
The Scots, although allied to Parliament, were known to be lukewarm in their support, and also had a strong attachment to the Stuart family (of which Charles was the chief). The Stuarts, after all, had been kings of Scotland long before they had inherited the foreign throne of England.