Now I might not know about designations, but I do know that:
Vulcan B.Mk 2 BS
A mini-fleet of 26 B.Mk 2s equipped to carry the Blue Steel missile equipped the Scampton Wing (that's 24 plus two spares). Blue Steel required modifications to the Vulcan’s spars, with the forward bomb bay spar having a crank in it, and the rear spar a cut-out. Bomb bay doors were removed and replaced by a fairing, and an extra ‘saddle’ fuel tank was installed in the bomb bay above Blue Steel’s forward section. A trials aircraft (XH539) was followed by 26 production ‘B.Mk 2 BS’ Vulcans. These were XL317-321, XL359-361, XL392, XL425-427, XL443-446, XM569-576, and XM594-595
Seven further conversions were made to cover a major modification programme on the Blue Steel Fleet, which left Scampton 'short'. These were XL384-390.
The seven 'extras' left Scampton with an embarrassment of jets after the mod programme had finished, and seven jets (XL445, 446, XM569-573) surplus to requirements were converted back to the freefall role in 1966.
Following the withdrawal of Blue Steel, all surviving aircraft were converted back to standard freefall bomber configuration.
Interestingly, these seven extra Blue Steel conversions were the only aircraft delivered with 201s that were officially converted to have 301s - this mod being undertaken at the same time as the Blue Steel mod, when the aircraft were stripped down to their undies anyway.
I make the 301 situation as follows:
Almost all Vulcan B.Mk 2s (from the eleventh aircraft, XH557, onwards) were built with larger engine intakes, in anticipation of the greater mass flow demanded by the 20,000-lb st Olympus 301 engine, though most were actually fitted with the 17,000-lb st Olympus 201. The 301 also required major structural alterations to the engine bays, making re-engining a complex and difficult process, requiring a full return to works. 36 aircraft were built with Olympus 301s, and seven more received them during conversion to B.Mk 2BS.
Trial Installation: XH557
Proof Installation: XJ784
Fitted on the production line during build: XL391, XM574-XM657
Retrofitted: XL384-390
When it comes to Skybolt, things are less clear.
XH537, XH538, and XH563 were trials aircraft ('563 for electrical compatability, so perhaps not fitted with pylons, etc?).
XM597-612 were built with the required hardpoints and wiring for Skybolt (16 jets) as was XL391 (the first Olympus 301 aircraft, held back on the line as a result).
But there were supposed to be 18 fully fitted Skybolt aircraft, and various sources list the following as having full Skybolt mods (front and rear attachments, etc.)
XL390, XH555 and XM574.
To further muddy the waters, most XH- and all surviving XJ- serialled B.Mk 2s were subsequently retrofitted with Skybolt front attachment points (not rear) in 1964-65, though this was after the (1962) cancellation of Skybolt.
And while the B2A designation may have been unofficial it was clearly used, but for which - Olympus 301 jets or Blue Steel? Does anyone have a B2A in their logbook under 'type'?