The XJ12 and XJS certainly were that bad. The electrics are suprisingly sound, though - mostly because unlike the other British marques, Bosch supplied most of Jaguar’s electrical components, like the fuel injection system. Other British manufacturers, including the other BL marques, used British-made Lucas parts, which were horribly unreliable.
Johnny LA pretty much nailed the second part of the question; essentially, what happened to the British motor industry was British Leyland. It was basically a merger of all the important British-owned car manufacturers under the auspices of the Labour government, with the idea being that successful (and profitable) Leyland would be able to revive the rest of the British motor industry, which was struggling.
It might have worked, except that in 1975 it was partly nationalized, and the British motor industry had most of the same problems in the seventies that the US industry has today - a mostly unionized workforce, with the associated increases in manufacturing costs and so on.
Of course, during the seventies, most of Britain was going on strike half the time anyway. BL management probably spent more time negotiating with the trade unions than it did planning new cars and so on, with the predictable result being that the cars that did actually get build were poorly designed, poorly built, and largely thought out with little or no regard for consumer demand or market trends.
In addition, lots of the consolidated brand names were previously competing with each other, and BL made little or no effort to rebrand them or keep them from competing on price.
In effect, each brand was stealing market share from the other BL brands rather than competing with non-BL entities.
Into this clusterfuck arrived the Japanese, who were making cars just as cheaply as the British, but without the shitty build quality. And with less beige in the interiors.
The eventual result was that during the 80s, the BL brands (and BL itself) were slowly divested and sold off, until one day Honda was the majority owner of the (then-renamed) Rover Group, which has itself been sold off piecemeal to the point where nobody really knows who owns what.
A Chinese company owns about half of the old BL brands, but most of them haven’t actually been used in over 20 years (like Triumph, Wolseley, BSA, MG, Morris, Rover, and so on), and the original factories have all been sold off or knocked down. Rover’s Cowley plant is still in use- that’s where the current Mini is built- but AFAIK that’s all that’s left of BL.
It’s not as though there are no carmakers in Britain; Ford, GM, BMW, and all the Japanese companies have factories or design studios there. Ford’s European operations are mostly run from Britain, although few of the cars are actually built in Britain. Vauxhall, which has been around since something like 1921, is GM’s UK subsidiary and sells the models which are badged as Opels in Europe in Britain; they’re also responsible for designing most of them.
Until fairly recently, sports car manufacturer TVR was thriving as an independent company, but has since gone bust and is now owned and operated by a Russian kid.
There’s still Morgan, which builds horribly old-fashioned cars out of wood and sticks a whacking great V8 in them. I hate the things, but there’s a ridiculous waiting list for their classic models - something like 2 years, I think. My dad ordered a Morgan in 1981, then found out he was having a second child (me), and sold his spot in the order queue for several hundred pounds- a not inconsequential sum at the time.
ETA: Forgot to mention- Rolls-Royce and Bentley soldiered on as British-owned companies (subsidiaries of the aerospace company Vickers, which is now BAe) until 1995 or so. Now they’re owned by BMW and VW, respectively.