Are you sure about that? Everything I can find says that the Vulcan (in its various B1 and B2 guises) used the Bristol Siddeley Olympus 101, 102, 104, 201, 202, 203, and 301 engines. Some Vulcan testbeds also flew other Olympus variants in the bomb bay to undertake inflight testing for the TSR2 and Concorde.
The Rolls-Royce Spey apparently entered service in 1968 according to
Rolls-Royce's website which was 16 years after the Vulcan first flew in 1952, and 12 years after the aircraft officially entered service.
Because development of the original Olympus was behind schedule, Rolls-Royce Avons and later Armstrong Siddeley Sapphire engines were also used in the Vulcan for testing, but both of these engines produce substantially lower thrust than the Olympus, so could never have been used in the production version of the Vulcan.
(Incidentally, Speys were used in Thrust SSC.
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