The practice has its distant origins in Jewish religious law, which requires women to undergo purification by ritual bath (mikveh) after giving birth as well as monthly. See Leviticus Chapter 12. For those interested, here's a link to an explanation.

For a woman who has borne a son, Leviticus prescribes a wait of 33 days after circumcision, which takes place on the 8th day after birth, or 41 days in all.

The Feast of the Circumcision of Jesus falls on January 1; Candlemas, the Feast of the Purification of the Virgin Mary falls on February 2, 33 days later, and 7 days after Christmas. That would explain the 40 day/6 week post-birth interval in traditional Anglican practice.