In addition to Harper's answer, if the insurance company also gives you the runaround, here are some reasonable next steps:
Write down everything. Focus on the facts; don't editorialize or write your opinions, just put down what actually happened. Keep any written documents which can corroborate your story.
Keep talking to both the hospital and the ...
Waiting two years is weird. However it's possible that this whole thing got a 15-month "pause" because of the pandemic, and that would make the timing more plausible.
Regardless, do not let this stress you out. It's just a normal and common billing snafu.
Contact your (old) insurance company
The old company will cover the claim because the event ...
No, in the U.K. unless you have bought dental insurance then there is no way to claim that money back or deduct it from any kind of tax.
If you sign up for private dental insurance then you pay a monthly fee and can submit the receipts to the insurer for a partial refund.