DHfan,
IF BEA had done as you suggested they would have been left with an aircraft and no launch customer. For all of the 'comparing the US designs to UK designs' it is often forgotten that the US launched all of their commercial airliners on a customer airline requirement with designs entirely customised around those airline requirements. So may be it WAS the fact that the UK state airlines were rubbish at traffic and market forecasting?
Don't forget too that long after the launch of the Trident, when BEA were looking at the Trident 3 and 1-11 500, they had to be effectively bribed by the Govt into taking UK built aircraft in the shape of compensation and subsidy payments to get BEA to order Trident and 111, when what they wanted, and tried to order, were Boeing 727 and 737's. That fact was widely publicised at the time and can not have helped BAC and HSA in their marketing efforts.
As to the VC10, again we can lay some of the blame at BOAC, the folks who specified the hot and high for Commonwealth routes nonsense, which Vickers went with, and none of them had any notion at all that these airports would all be extended to take 707 and DC-8's, thus rendering the VC10 obsolete before it had even entered service.