Impossible to surpass Bergerie1's welcomed first-hand experience there, but digging around the bookshelf on a wet Saturday afternoon does suggest that Capt Tom Stoney was one of BOAC's leading lights and a pretty frequently-occurring name in the generation after OP Jones but alongside the likes of "Flaps" Rendall.
Speedbird - The Complete History of BOAC by Robin Higham (finally published in 2013 after being commissioned 53 years earlier) is more of the politics and board level goings-on and doesn't really mention individual pilots - even OP Jones merits only one mention!
Sir Basil Smallpeice's autobiography - Of Comets and Queens (Airlife Publishing 1981) is probably the most enlightening (and helped by a decent index). Sir Basil makes generous mention of those around him, with Tom Stoney appearing four times:
July 1956 as part of a team sent to Boeing to evaluate the 707 -
"We felt that insufficient work had yet been done on the Douglas DC-8. On the other hand the Boeing 707 was well advanced, and we believed the claims made for it. But to be as certain as possible, we sent a twelve-man team to the West Coast during July. It was led by Alan Campbell Orde and included two of our senior line pilots, Capt Tom Stoney and Capt Tommy Farnsworth. On returning at the end of the month they reported unanimously that the Boeing 707 was the best aircraft for our purposes - particularly when powered by Rolls-Royce Conway engines. These would help its performance and reduce the amount of dollars needed."
October 1958 as the Captain of the inaugural Comet 4 service from New York to London after several delays in obtaining Port Authority approval to fly the jet from Idlewild which finally came through on the day before, announced by Smallpeice standing on a chair in the Speedbird Club in New York where an aircraft and crew were on standby:
"So, on Saturday, 4 October, 1958, BOAC made aviation history by operating the first transatlantic jet service ever - and, to cap it, both ways on the same day. Capt Tom Stoney, our Comet flight manager, in command eastbound, took the aircraft up to 1,850 ft while still inside the perimeter fence of the airport, at which point he throttled back to reduce the noise level within limits acceptable to the authorities.
Out over the Atlantic, we passed the other aircraft, out of sight, with Pops d'Erlanger on board and Capt Roy Millichap in command. Our eastbound flight to London took only 6 hours 12 minutes, thanks to a tailwind of 92 mph and the priority given us by Air Traffic Control over the UK. The aircraft glided in to a beautiful touch-down. A warm welcome was given us on the tarmac, and it gave me a particular glow of pleasure to find Miles Thomas amongst those who had come to greet us."
April 1960:
"BOAC's first Boeing 707 arrived at London Airport on 29 April 1960 under the command of Capt Tom Stoney, by now manager of the 707 Flight. The incorporation of special "hand-made" mods had delayed delivery by only four months. We began to put them into transatlantic service on 27 May."
And finally, Smallpeice's book has an appendix listing all BOAC Royal Flights between 1951 and the end of 1963, when he left BOAC. [He did later become Chairman of Cunard overseeing its order for the QEII and in 1964, was appointed as an advisor to Buckingham Palace, so the Royal connection continued.] Capt T B Stoney is listed once, flying a Comet 4 on 28 October 1958 from London to Ottawa with the Duke of Edinburgh and then 1 November 1958 from Ottawa to Leuchars.
Noting the comments above, the Smallpeice list shows Captain R C Parker and Captain R G Ballantine taking the Argonaut from London to Nairobi on 31 January 1952 with Princess Elizabeth and the Duke of Edinburgh, and the same two Captains returning on 6-7 February from Entebbe to London with Queen Elizabeth II and the Duke of Edinburgh. It doesn't show other members of the crew so entirely possible that Tom Stoney was among them, but if so, he was not the Aircraft Commander on that occasion.
In case of interest, other BOAC Captains listed on the Royal Flights:
O P Jones, R C Parker, R G Ballantine, A M A Majendie, E Rotteram, W N C Griffiths, A P W Cane, R R Rodley, A C Loraine, F A Taylor, P C Fair, R C Parker (again) and R G Ballantine (again), C B Houlder, R E Hallam, L V Messenger, F Walton, A S M Rendall, J J Veasey, R I B Winn, G Store, J R Johnson, J Woodman, B C Frost, W J Craig, F E Flower, D Smith, D Anderson, J T Percy, A Meagher, A P W Cane (again), G G Stead, J L Gregory, N A Mervin-Smith, D A Cracknell, R E Hallam (again), B G Wallace, R E Millichap, E J N Hengle, J T A Marsden, B E P Bone, J A Kelly and R H Tapley.
Third BOAC source book - BOAC - An Illustrated History by Charles Woodley (2004, Tempus Publishing):
First mention of Captain Stoney in this publication is in connection with the Comet inaugural, giving a near-identical account to that in Sir Basil's book and so not reprised.
Second mention gives more detail of the 707 entry to service at BOAC and the part Capt Stoney played in it:
"BOAC's first Boeing 707, G-APFD, arrived at London on its delivery flight from Seattle on 29 April 1960. Under the command of Captain T.B. Stoney, BOAC's Manager, 707 Flight, the aircraft made the 4,900-mile journey non-stop in 9hrs 44 mins. Crew training was carried out at RAF St Mawgan, Newquay, and on from 3 May 1960 a series of proving flights was operated between New York and London via Prestwick. The first such flight was operated by G-APFD under the call-sign Jet Speedbird 001. Proving flights were also operated from London to Toronto via Prestwick, the first such flight, by G-APFD as Jet Speedbird 010 on 17 May 1960 inaugurating the new extension to runway 13/31 at Prestwick. On 27 May 1960, Captain Stoney commanded G-APFD on the inaugural BOAC Boeing 707 scheduled service, from London to New York. The next day, Captain Nisbet was in charge of the same aircraft on the inaugural eastbound service."
The last BOAC Comet 4 flight on 24 November 1965 (Damascus-London) was commanded by Captain R C Alabaster as the Manager, Comet Flight, who had also flown the latter legs of the 1952 Comet 1 inaugural from London to Johannesburg, taking over the aircraft at Khartoum to fly to Entebbe, Livingstone and Johannesburg. Clearly some pilots stayed on the Comet throughout, where Captain Stoney had moved from Comet to 707 as Fleet Manager on both types in succession.
And many of those listed above have relatives flying today - I can think of at least two!
Hope this helps and may be of interest.