Inheritance tax was increased substantially by the Finance Acts of 1894 and, particularly, 1909-10 (which sparked a constitutional crisis when the Lords refused to pass it) and the latter legislation also introduced capital gains tax (in effect) on land sales. Together, that meant that property needed to generate enough of an income to pay the taxes that would arise on transfer whether by inheritance or by sale.

The first world war and its aftermath killed a lot of men, both from the land owning classes and their workers. Contrary to the impression of cowardly officers relaxed about the death of the proletariat, a trope with a longer history than Blackadder, it was front-line officers who died in greater proportion. 12% of private soldiers were killed in the first world war, but 17% of officers and 20% of old Etonians who served. Commissioned officers were often from land-owning families, which were weakened by their loss. And of course although no-one would paint the post-war economy as a workers' paradise -- the General Strike gives the lie to that -- wages had risen substantially [1] which made it harder for the great houses to keep their workforces.

Some large houses staggered on into the 1970s or even 1980s, but the wage bill required to run them, along with the tax bill due when the next generation inherited, meant that most of them ended up transferred to the National Trust in lieu of death duties. Sometimes there was a life interest for a small apartment for the former owners as at Plas Newydd, but in general the old landed gentry retreated off the land and those that remained were leading very different, smaller, more commercially aware, lives. Some of the houses were demolished, some were adapted for other purposes, many were just slowly decaying.

Some of the acquisitions by the National Trust were in a pretty sorry state by the time they were transferred: an interesting example is Calke Abbey, which was handed over in 1985. That had been decaying with the owners in situ and has been kept by the NT in roughly the state it was in at that point. Others had been requisitioned during the second world war and then essentially abandoned: examples of this would be Compton Verney, which sat empty and rotting from the end of the war until its purchase by the Moores family in the 1990s, and Croome Court, which bounced between owners including the Hari Krishna movement until it ended up with the National Trust (on a long term lease: It's Complicated) about ten years ago.

So the tl;dr would be that the houses couldn't generate the revenues to pay the wages of the staff and the taxes imposed by governments no longer quite as deferential to the aristocracy as they had been, so they were progressively sold, handed over to the government, or left to rot.

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[1] https://api.parliament.uk/historic-hansard/written-answers/1925/jul/30/average-weekly-wages