There is a William WINNE baptised in Plymouth St Andrew in 1799 (parents William & Mary), so might be their child.

Annoyingly, neither baptism shows the father's occupation.

I am not sure about the burial of William Winn in Essex...

FMP has the record of a prisoner of war named William Winne of 'Shiffield' and the corvette Cavalier but he arrives in camp on 26th May 1811. He is describes as the servant of Mr Taylor, so he might not have been a marine (though William could have left the service some time after his marriage to Mary Williams).