G'day,
Here's how Child recounts the legend, with one small addition by me, American spelling corrected by my spell checker :). I'd suggest a copy&paste, print & read offline:-

This story of Beichan, or Bekie, agrees in the general outline and also in some details, with a well known legend about Gilbert Beket, father of St Thomas. The earlier and more authentic biographies lack this particular bit of romance, but the legend nevertheless goes back to a date not much later than a century after the death of the saint, being found in a poetical narrative preserved in a manuscript of about 1300.

We learn from this legend that Gilbert Beket, in his youth, assumed the cross and went to the Holy Land, accompanied only by one Richard, his servant They "did their pilgrimage" in holy places, and at last, with other Christians were made captive by the Saracens and put in strong prison. They suffered great hardship and ignominy in the service of the Saracen prince Admiraud. But Gilbert found more grace than the rest; he was promoted to serve the prince at meat (in his chains), and the prince often would ask him about England and the English faith. Admiraud's only daughter fell in love with Gilbert and when she saw her time, in turn asked him the like questions. Gilbert told her that he was born in London; told her of the belief of Christians, and of the endless bliss that should be their meed. The maid asked him if he was ready to die for his Lord's love, and Gilbert declared that he would, joyfully. When the maid saw that he was so steadfast, she stood long in thought, and then said, I will quit all for love of thee, and become Christian, if thou wilt marry me. Gilbert feared that this might be a wile; he replied that he was at her disposition, but he must bethink himself. She went on loving him, the longer the more. After this Gilbert and the rest broke prison (with the daughter's help according to another account I read - A of A) and made their way to the Christians. The prince's daughter, reduced to desperation by love and grief left her heritage and her kin, sparing for no sorrow, peril, or contempt that might come to her not knowing whither to go or whether he would marry her when found, and went in quest of Gilbert. She asked the way to England, and when she had come there had no word but London to assist her further. She roamed through the streets, followed by a noisy and jeering crowd of wild boys and what not, until one day by chance she stopped by the house in which Gilbert lived. The man Richard, hearing a tumult came out to see what was the matter recognised the princess and ran to tell his master. Gilbert bade Richard take the lady to the house of a respectable woman nearby, and presently went to see her. She swooned when she saw him. Gilbert was nothing if not discreet: he "held him still," as if he had nothing in mind. But there was a conference of six bishops just then at St. Paul's, and he went and told them his story and asked advice. One of the six prophetically saw a divine indication that the two were meant to be married, and all finally recommended this if the lady would become Christian. Brought before the bishops, she said, Most gladly, if he will espouse me; else I had not left my kin. She was baptised with great ceremony, and the marriage followed.

The very day after the wedding Gilbert was seized with such an overmastering desire to go back to the Holy Land that he wist not what to do. But his wife was thoroughly converted, and after a struggle with herself she consented, on condition that Beket should leave with her the man Richard, who knew her language. Gilbert was gone three years and a half, and when he came back Thomas was a fine boy.

That our ballad has been affected by the legend of Gilbert Beket is altogether likely. The name Bekie is very close to Beket and several versions A, D, H, I, N, Set out rather formally with the announcement that Bekie was London born. Our ballad, also, in some versions, has the Moor's daughter baptised, a point which of course could not fail in the legend. More important still is it that the hero of the English ballad goes home and forgets the woman he has left in a foreign land, instead of going away from home and forgetting the love he has left there. But the ballad, for all that, is not derived from the legend. Stories and ballads of the general cast of 'Young Beichan' are extremely frequent.

Cheers,
Alan