Private dental insurance in the U.K. doesn't cover as much as you think.
Edit: Pretty sure I pay £30 odd a month and I've had root canal treatment, new crowns, etc.
If you need a simple crown that is subsidized if not completely by the NHS you'll be able to offload it to the insurance pretty easily, if you want the top of the line ceramic crowns that cost 1500-2000 GBP no insurance will actually cover that.