And by the way, that is how it works even in places with socialised healthcare. It's not like anyone is going to prevent you to buy private insurance in the UK if you have the money.
By the way, that is not how it works in Canada. Seems it's not legal to pay for additional access. Private insurers are used for drugs, paramedic bills, and other things not covered by the province; but they can't pay for enhanced medical services, only coverage of out-of-pocket expenses.