> The Queen does not own all of the UK.
That depends on what you mean by “own”, and “the Queen”. The Crown, that is, the monarch in official capacity, holds ultimate title to most land in the UK (IIRC, the exceptions are some parts of the Orkney and Shetland Islands), but exercises the rights associated with that title, like many other rights and powers, on the advice of the government ministers (and in practice through government officers), rather than unilaterally, at risk of Constitutional crisis.
The monarch, as a corporation sole, owns the Crown Estate, in something more like private ownership, but for quite some time the rights of ownership of the Crown Estate have been exercised by a government-appointed body, with the monarch personally receiving a share of the proceeds and being relieved of the burden of funding government operations, for which they were previously responsible.
The monarch also has private estates, which are owned so what like typical private holdings, except the usual expectation of neutrality on legislation does not apply where legislation impacts the private estates, and so the monarch has an effective and quietly exercised veto on legislation to the extent that it impacts those estates.