Minus Airbus which is a group of companies, why does the United Kingdom not produce aircraft anymore ie, the VC10.
The root of the reason is the fact that aircraft design has become very expensive and the world economy cannot support more than a few companies anymore.
Look at other industrialized countries: They all used to have scores of aircraft companies, which all merged or went down over time. Russia might seem an exception, but the Russian design bureaus are not very productive anymore and kept alive artificially. By now, a national economy the size of Great Britain is too small to support even a single commercial jet builder.
In Augustine's Laws, Norman Augustine shows how aircraft prices have historically accelerated at a faster rate than the economy, and driving this to it's ultimate conclusion, he predicts for the US military:
In the year 2054, the entire defense budget will purchase just one tactical aircraft. This aircraft will have to be shared by the Air Force and Navy 3½ days each per week except for leap year, when it will be made available to the Marines for the extra day."
There is no conspiracy about it, economics is enough for a convincing explanation. If there is a culprit for the early death of many British aircraft makers, it would be the British Government bureaucracy itself, with a helping hand given by BOAC management. Britain effectively nationalized her aircraft industry at the onset of WW II, and left it to Government bureaucrats to decide which aircraft to build next. This produced aircraft like the Saunders-Roe Princess or the Bristol Brabazon which incorporated many innovations, but were conceptually completely behind their times. When they once tried to be visionary, they steered all efforts into supersonic airliners, which also proved to become a dead end.
When British designers tried to design jet airliners, BOAC management saw no market for a jet airliner but bought the Boeing 707 less than a year later. If you desire to see a conspiracy behind the early death of many British airliner projects, maybe start looking here. The EU certainly has nothing to do with it.