The UK and Spain have a private health sector with Clinics, GP, ... To access those you either need to pay cash or have a private health insurance.
Both the UK and Spain have also a public health sector, with Clinics, GP, ... that is accessible for free.
In the UK and Spain, very few private health insurances covers Birth or Emergency Care: for those you are supposed to go to the public service or pay cash in a private clinic.
Other countries like Belgium have health insurances that give you the kind of extra comfort you mention. But they cost something like 5 EUR a month vs the 100 EUR in Spain and the UK.
