I remember as a pax on a flight back from Bangladesh, the gear stayed down for half an hour after take-off for that reason.
I suspect your memory is playing tricks! Leaving gear down for 30 mins would be a big problem, slow speed, low altitude. The flight probably transited Calcutta for Dacca and the F/E told the Captain on the walkaround that the brakes felt rather hot! It wouldn't have been for more than 10 mins absolute max! It had no problem with hot brakes, but you would take care on short sectors.
The VC10 does hold a special place in my affection. It was a lovely plane with no vices. We had a far better world coverage than BA has now- round the world trips. The Conways were ultra reliable, but the surges were extraordinary! They always self recovered. It was ultra comfortable, supremely quiet (up front), and incredibly stable- there was no 'shudder' or shake at all inflight. All in all, a thoroughly splendid aeroplane to tour the North American colonies and the pink bits on the world map!