I stumbled across this City of London archive film from 1970. The footage is a bit wobbly but well worth watching. There's some footage of the Golden Lane Estate halfway through - it all looked so clean back then! (Apologies if this film has been posted before).
Some highlights include a dirty looking Guildhall, views of St. Pauls from all angles, smoking in the workplace, Routemasters, retro cars, burning buildings, typewriters and not a Barbican tower in sight!
Meanwhile, I really recommend this one too - lots of great footage of Golden Lane in construction, and I love the window cleaners stopping by for tea halfway up Great Arthur House!