The shortest-lived and shortest distance Red Arrow was the 511 from Victoria Station to Victoria Coach Station. It ran from 1st July to 7th October 1972. The route number was later reused for a service from Victoria to Waterloo. Various operators have had a go at linking the coach and rail stations but no service has been sustainable.
This was a report in "Commercial Motor" magazine in March 1967:-
London Transport this week out lined its proposals for the first of the suburban "satellite" schemes under its big plan for reshaping the central (red) bus services. Stage one of the Wood Green scheme is planned for introduction towards the end of this year. It will bring about major changes to bus services in the area, which is served by two tube stations on the Piccadilly Line (Wood Green and Turnpike Lane) linked by Wood Green High Road with its busy shopping district. LT plans to bring in four flat-fare routes operated by single-deck buses with coin-operated entrance gates.
But it was in September 1968 that the flat fare standee services was introduced based (loosely) on Wood Green Underground station. W1, W2, W3, W4, W5 and W6 all replaced or enhanced local routes.
The seasoned view is that the "reshaping" model was not successful. We Brits simply don't like "standee" public transport; the turnstiles didn't work very well and here were hold-ups. Passengers did not like changing because, as well as the inconvenience, it was perceived that journey times were longer.
It is no surprise, then, that of these only W3 (now double deck) ...