The actor was caught breaking the 20-mile per hour speed limit in Earls Court last October.
His Audi was clocked by a speed camera at 28mph as he drove towards West Kensington on the A4.
He admitted being the speeding driver but submitted the form to the police too late to avoid a criminal prosecution.
He pleaded guilty to the offence and was sentenced at a private court.
Redmayne received three penalty points on his licence and must also pay £130 in costs and a £400 victim surcharge.
