What evidence is there that Edmund was born in 1538? It seems as though this is the traditional LDS member trick of deducting 25 from the date of the marriage. The marriage is only on the IGI as member submissions - have you checked the parish register to see if it actually appears?
John Ashwell of Totternhoe was executor of the will of William Tevett of Totternhoe, dated 14 Aug 1505, so there were Ashwells in the parish prior to 1558. Thomas Aschewell was a witness to the will of Richard Puttnam who desired to be buried at Totternhoe, dated 20 May 1530
I can't find any trace of the name Ashwell in the Totternhoe entry in VCH Beds,
David
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Census information is Crown Copyright, from www.nationalarchives.gov.uk Beds: Cople: Luke/Spencer Everton: Hale Henlow: Cooper/Watts/Sabey Potton: Merrill Southill: Faulkner/Litchfield/Sabey Woburn/Husborne Crawley: Surkitt Hunts: Gt Gransden: Merrill/Chandler/Medlock Toseland: Surkitt/Hedge/Corn Cambs: Bourn: Bowd Eltisley: Medlock Graveley: Ford/Revell