Apart from the entry in British History online for Bishop's Stortford the only other reference I have found linking a Hawkins/Hawkyns with Piggotts is the Will of Edward Hawkyns the elder of Stortford which was made 27 May 1659/proved 9 April 1660 in which he refers to the 'manor of Piggott which I late had and purchased of Robert Salmon' which supports the British History online article.
There are no Hawkins/Hawkyns pedigrees in either the Visitation of Hertfordshire or the Visitation of Bedfordshire and there are no early references to the name in the online catalogues of the record offices of Hertfordshire/Bedfordshire.