Hello Phil,
I've searched all probate records available through Ancestry and Find My Past, and the National Archives, and found nothing for him. While he was related to the Hall End Lakin's I think he may have been a 'poorer cousin'. It was his sister Mary who married into that family (married James Lakin in 1747). His older brother Thomas seems to have been very successful, as his will is extensive and he leaves considerable assets and money to his nephews and nieces, including Benjamin's children. My thought was that Benjamin's family connections would have meant a good marriage, so Mary (Green) may have come from a good background. One can only guess.
Thanks for your suggestion. Perhaps there is a will out there somewhere for him, just not in online records.
Kelly.