Hello Barney
According to Dennis' Royal Aircraft Establishment at war (2008 ), Brown was the Chief Naval Test Pilot, RAE Farnborough, 1944-49 and CO Aerodynamics Flight 1947-49. The High Speed Flight Section began to investigate the problems experienced at near sonic flight speeds early in 1943. The aim was to establish the max Mach No which could be achieved by a particular aeroplane. The Mustang used was Allison engine P-51, the book doesn't give more exact type, it only notes that dive started from 28,000 ft only due to a/c ceiling limitations. Also on P-47 and -38, no subtype is given, only notes in both cases that Dive recovery flap investigation and additionally on P-47 Very high stick forces.
In his memoirs Wings on my sleeve, 2006 edition, Brown only writes that at the end of 43 (before Christmas anyway) he was transferred to Boscombe Down. 5-9 Jan 44, he visited Italy to testfly Italian a/c, when back he began his 4-engine training on Short S29, on 17 Jan he reported at Farnborough because the previous naval test pilot there had just been killed on the rocket Seafire. So he joined the famous Aerodynamics Flight on 17 Jan 44. And yes, he writes that the transonic flight testing took on a new emphasis after a visit to RAE early in 44 by Lt. Gen. Doolittle, who had just taken over command of the 8th USAAF which had suffered worrying escort fighter losses when the fighters on high cover dived down to intercept LW fighters and lost control. There was no time to set up a normal instrumented research program, but what was wanted was a hand-on series of tests on the P-38H, P-47C and P-51B. The tests up to their tactical and critical Mach numbers began in late Jan 44 and continued through to early March 44. So according to Brown these tests were not part of the famous scientific tests by RAE I mentioned at the beginning of this message.
HTH
Juha