@ BN2A
I'm sure the real experts will "adjust" my understanding - but I believe Concorde, loaded for the transatlantic "Sierra" routes, could hit about 5000 fpm peak VS when climbing at 400 KIAS between ~10,000 and ~28,000 feet (wherever 400 KIAS = M 0.99). Leaving a coastal airport (New York, Barbados, Dakar), she would quickly be clear of land and could more or less transition directly through Mach 1 as soon as she reached 28-30,000 feet.
Those 4 Olympus engines could maintain Mach 2 with no afterburner at 50,000+ feet, so they had tons of excess power down low. Again my understanding is that they stayed at 100% dry thrust from brake release until TOD (except for subsonic cruise segments), with the AB added for takeoff, and when accelerating from Mach 0.96 through Mach 1.7.
Mach 2.00 was reached in about 30 minutes @ ~51,300 feet, depending on atmospherics - a relatively long slow slog compared to the initial climb and acceleration.
From inland airports such PDG or Heathrow, there was a "pause" for level subsonic cruise (M 0.94-0.96) in the high 20s until clear of the coastline by 20 miles (over La Manche or the mouth of the Bristol Channel.)
@ leb001 - greenhouse visor, BA livery, and short tail - probably G-AXDN (aircraft 101). Although I'll defer to the experts, as always.