You mention the WI which like you say is Women only unlike the Mothers Union which is open to all it appears...
maybe its time for change all round and to make things inclusive and that is what Mssrs Fry and Knopfler want to do with the Garrick Club.
Maybe the Garrick Club can take a leaf out of Marylebone Cricket Club which from 1787 until 1998 was a solely male orientated club. In 1998 Women were allowed as members and by all accounts the MCC is flourishing!