From the Mayflower History Website, http://www.mayflowerhistory.com by Caleb H. Johnson:
Bartholomew Allerton was born around 1612 or 1613 in Leiden, Holland, to parents Isaac and Mary (Norris) Allerton. He, his parents, and his sisters Remember and Mary came to Plymouth on the Mayflower in 1620. At some point, Bartholomew returned to England and took up residence in Norfolk and later Bramfield, Suffolk. A 1657 chancery suit, a couple of letters in the British Library, and his 1658/9 will are the known records of his life in England. Nobody has successfully documented a descent from Bartholomew Allerton, but he probably does have some descendants living in England, if information about his children could be further traced.