Alan Cook yDNA
Y chromosome DNA haplogroup J2a
Derived J M304, J2 M172, J2a M410 positive
Ancestral J1 M267, J2a1a M47, J2a1b M67, J2a1e M158, J2a2 M340 negative

Cook Genealogy DNA List (Group 23 is my genetic match)

According the Internet, Haplogroup J2a was not common in England, but there in small numbers. Could have been there for thousands of years before the Romans, having traveled with Neolithic people to the occupied region.