Episode 6: Many Happy Returns
"Patrick McGoohan is seen walking along Park Lane with a number 88 Routemaster sporting a Typhoo Tea advert behind him. There's also another Routemaster just before it but I didn't catch details of that." (thanks Simon Quinlank)
In truth there's not much to see:
...but immediately prior to this there is a glimpse of a Green line Routemaster:
Episode 17: 'Fall Out':
In the finale episode the Prisoner is seen crossing the road outside the Houses of Parliament behind a passing London Transport XA class Leyland Atlantean.
The Prisoner runs down the road; he is then seen clambering onto a London Transport AEC Routemaster/Park Royal of the xxxCLT batch on service 59: