At one time, all non-regular Officers were permitted to wear the beret in No2 dress / BD.
SD peaks in No2 dress were optional for Officers on non-regular commissions, although the majority of such officers tended to emulate regular RAF officers, and consequently wear peak caps (this became even more ingrained as a behaviour once forage caps were no longer permitted to be worn in No1 HSD)
The RAF Regiment, and in particular the RAF Regiment branch of the RAFVR (following the original raising of that Regiment, see article linked below) became particularly-keen on the beret as headgear, even well-before the end of WW2.
http://rs42.pbsrc.com/albums/e336/wilfsan/rafvrrgt-1.jpg?w=480&h=480&fit=clip
Reasons for this would’ve included parity with the large number of transferred/seconded Army Officers that joined the RAFVR (RAF Regt) who also wore berets, as part of their normal army uniform (topped-off, of course, with RAF Regt mudguards).
Prior to mid-WW2, the two categories of Air Force Officer that were most likely to be wearing SD peaks were regular RAF and AAF. The wearing of forage caps for all ranks (and especially for RAFVR(GD) Offrs and Men) became increasingly-popular.
However, the Training branch of the RAFVR were particularly unhappy about the fact that AP1358 (back then, an Air Force Officers’-only dress publication) required them specifically not to wear SD peaks whilst on parade, stating that they could only wear forage caps under such circumstances. A great deal of lobbying went on, and eventually the AFB relented, allowing late and post WW2 RAFVR(T) to wear SD peaks on parade (like their brother RAF and RAuxAF Officers).
At some point (best estimate is around 1950, following the RAFVR relaunch in 1947) forage caps ceased to be issued, and berets became the standard No2 dress headgear for all Other Ranks (except certain key trades including RAFP and MTD), and were meant to be standard No2 dress headgear for RAFVR Officers. However, they still had the option of wearing SD peaks in No2 / BDBG, an option they tended to frequently favour, so as not to lose status in the face of their cap-wearing regular and Auxiliary fellow officers.
Throughout all this time, forage caps remained an optional alternative in No2 dress, but dipped very much out of favour other than amongst aircrew into the 1960s.
Another factor that pushed the adoption of the beret within the broader RAF (led from the front, by the Regt) was the universal initial issue of berets to RAF(National Service) personnel, irrespective of being commissioned or Other Ranks, at entry.
And of course, as we all should know (but have substantially forgotten) the majority of men who were called-up for RAF(NS) right into the mid/late 1960s, administered by the RAFVR(GD)…were, of course, aged-out ATC Air Cadets…who brought along their berets , classification badges and F3822s when they attested for Air Force Service…
wilf_san
EDIT
The punchline, regarding berets being worn by RAF Regt Officers in No2 dress, is that they substantially gained this right via the RAFVR. And ironically, the loss of that privilige generally amongst reserve Air Force officers appears to have been as a result of a clumsy-worded Amendment to the RAFVR(T) SD Peak Cap prohibition paragraph being revoked in a 194(4?) edition of AP1358