Bus 408

Operated by Falcon Buses running between Epsom and Cobham (including Sainsburys Cobham and Tesco Leatherhead). 

Bus 479

Surrey County Council has published the full timetable for the 479 route through Leatherhead Ashtead Fetcham and Bookham from 18th December covering both the Mon-Sat service to be operated by Falcon Buses and the Sunday service with Stagecoach.
The main change is Saturdays to follow weekday pattern of hourly with "Bookham shorts" i.e. Epsom-Bookham and Bookham-Epsom. 
Falcon Buses have a timetable app for Apple and Android smart phones. The app can be downloaded in the Apple and Google app stores.  Search for Falcon Buses in the stores.

Bus H1

Operated "In House" by the Hospitals running between Epsom, Sutton and St Helier Hospitals from Monday to Friday (excluding bank holidays) from around 6.25am until 7.50pm.

Bus 21

Operates from Crawley, Charlwood, Newdigate, Dorking, Boxhill, Leatherhead Ashtead through to Epsom.