St Bride’s Church is a church in the City of London, England. The building’s most recent incarnation was designed by Sir Christopher Wren in 1672 in Fleet Street in the City of London, though Wren’s original building was largely gutted by fire during the London Blitz in 1940.Wikipedia
I have found this church is nearly always open on a week day but never on weekends, despite what there website says. It has a crypt which is well worth exploring.
Opening Times: Mon to Fri 8am-5pm Sat 11am-4pm Sun 9.30am – 6.30pm
Nearest stations: City Thameslink, Blackfriars and St Pauls.