Enfield are managed by former West Ham boss Marc Nurse and reached the last eight with a narrow 3-2 victory at the up and coming Harlow Town, while the Hammers had a bye.
The Premier League Southern hosts saw off their South East Division 1 visitors on Wednesday 14th December with two efforts by Chloe Burr, after the recent attempt to play the tie had been thwarted by a frozen pitch.
The Hammers will now take on Tottenham Hotspur in the semi-finals of the Ryman Women’s League Cup (sponsored by Boux), while Charlton Athletic welcome Worthing in the other half of the draw on Thursday 26th January 2017.
Spurs earlier thrashed Tonbridge Angels 12-1, Charlton put nine past Godalming Town and Worthing accounted for Burgess Hill Town by four goal to one.
