That were "grandfathered" in when the NHS was founded in 1947. There was a bit of a debate about it at the time I believe, but it didn't hurt the homoeopaths' case that the royal family have been big fans since the time of Good Queen Vic. Queen Elizabeth (later the Queen Mother) was a thoroughgoing woo.
There was a campaign to get the Glasgow hospital closed quite recently, which failed due to pressure groups complaining. However, there used to be five of these hospitals but now Tunbridge Wells is gone. Four green bottles, hanging on the wall....