JamesA & Seat62K
I know more about the 1-11 than the VC-10. The reason the One-Eleven was an (early) success was that it was designed for the world market and not specifically for the UK flag carrier. It was well established before BEA placed an order.
Three factors helped its demise:
1) the RR Spey engine was noisy and unreliable and American Airlines was foolish not to select the P&W JT8-D, which BAC offered. From then on the Spey was the only fit.
2) BAC treated it as a cash cow and didn't put in the investment necessary to compete with the rapidly advancing DC-9 and 737.
3) Once the DC-9 & 737 were in service, the US giants had the sales (& political) resources BAC couldn't match.