Greetings PGM and G2G!
Thanks to some really impressive research in 1998 by descendants of William Britton, we can be fairly confident that the William who married Mary Pendleton was not a son of James Britton and his wife Jane of Charlestown and Woburn—and that a brother Peter likely never existed at all.
Long story short, the claim originated in a sketchy Britton genealogy written 1901 and has been duplicated ever since, but is not supported by any primary or even pre-1901 sources. I've summarized the findings in William's, Peter's, James', and Jane's profiles, with additional references.
I've detached James Britton as William's father, but I'm not able to remove erroneous sons William and Peter from the PGM PPP profile of Jane (Unknown) Eggleton Britton Cole. Could one of the kindly PGM folks please detach them?
Might James Britton also merit a PPP? He was present in Charlestown and Woburn from 1640 and is subject to several (!) mistaken identities and disputes.