Free bike parking with security cameras
The City of London car parks provide secure parking free for bicycles (and motorcycles)
Baynard House near Blackfriars EC4V 4BQ: Free for bikes, 24h security, humans on site - extra bike racks outside glass fronted security office, accessible toilet (according to the Facebook group London Cycling)
Another recommended one is near the Barbican on London Wall EC2V 5DY which is an underground car park.
Other City of London car parks which provide free secure parking for bicycle are:
Minories E1 8LP
Smithfield EC1A 9DS
Tower Hill EC3R 6DT
For more information: https://www.cityoflondon.gov.uk/services/parking/motorcycles-and-bicycles
Paid for secure bike parking
This has been recommended on another websites: https://www.spokesafe.com
Some locations include lockers, repair stations, pumps and charging points for ebikes