When I first came to Leicester it was to work in the laboratory inthe Regional Cardiothoracic Unit back in the early 80s.
We did a lot of clever cardiac surgery including some 'breakthrough' research.
But I was shocked at how many patients were transferred to the NHS Intensive Care Unit from the local private hospital which did much more routine cardiac surgery - which of course was performed by exactly the same surgeons, usually on a Friday evening or Saturday. There was no overnight medical cover at the private hospital, so anyone with a hint of a problem was dumped on the NHS.
It still happens today.
Medical Tourism is another modern equivalent.