In most countries that have public care you can still do this, just like opting for private schools. Britain people buy private insurance for any additional services they want. But I don't think they usually get a tax incentives like private school does can in the US?
I don't know the state of your welfare services, but I suggest you consider it a tax. A tax you pay for those who cannot pay for private healthcare, retirement, etc. Additionally, you are covered in case you get into a bad accident, or you are down on your fortune.