St Mary-le-Bow is a historic church rebuilt after the Great Fire of 1666 by Sir Christopher Wren in the City of London on the main east–west thoroughfare, Cheapside. According to tradition a true Cockney must be born within earshot of the sound of Bow Bells. Wikipedia
I have always found this church to be open.
Monday to Wednesday: 07.30 – 18.00
Thursday: 07.30 – 18.30
Friday: 07.30 – 16.00
There is a cafe in the 1000 year old crypt.
Nearest tube stations: Mansion House, St Pauls and Bank.