Consistently with such a [supernatural] origin concerning this said Dyke, many and curious traditions are afloat. It is a weird, or wizard spot, upon its bank nothing of good omen happens. I have been told in perfect good faith, by one who dwelt near it, that on Grimsdyke the unhappy Jane Shore perished, being starved to death by King Richard's order, a baker being also put to death for his compassion in offering her a penny loaf. A curious connexion in which to find an historic name, and showing how great names and tragic events are rumoured amongst the people, though often, as in this case, in a distorted shape. That fairies make fun or make mischief, that ghosts and spectres have peculiar liberty on the soil of the Dyke, is the current belief of the country gossips.
Jane Shaw, in the 15th century, was mistress to King Edward IV. A paranoid King Richard accused her of stuff but as far as I can tell (from a quick internet trawl) didn't actually kill her off. Perhaps the story comes from another connected with 'shoreditch' in which, in a ballad, she dies.
Excerpt is from 'Records of Buckinghamshire'published by the Buckinghamshire Archaeological Society, 1858.