Sadly, only one of Australia’s 114 official National Living Treasures has ever appeared in an episode of Doctor Who.

It happened in 1978 during the incarnation of the fourth Doctor, played by Tom Baker. Instantly identifiable from his curly hair, trademark long scarf, wide-brimmed hat, penchant for jelly babies and robotic dog called K-9, Baker appeared in 172 episodes over the seven years of his tenure of the role. But in only one of his TARDIS-propelled adventures did he share the small screen with Gai Smith, a young Australian actress who subsequently became Gai Waterhouse, racehorse trainer and ongoing ornament to the antipodean track.

‘The Invasion of Time’ begins with the Vardans, a shape-changing race of green-helmeted near-humans, asking the Doctor to help them take over Gallifrey, home planet of the Time Lords. The Doctor agrees, but only as a ploy designed to outwit an invasion by the Sontarans, a bulbous-headed, green-blooded, three-fingered species of sinister, war-obsessed aliens.

Exiled to the Gallifreyan wastelands, the Doctor’s female sidekick, Leela, is captured by a band of back-to-basics proto-ferals known as the Outsiders. One of these shaggy, pelt-wearing hunters is Presta, played by 23-year-old Gai. Togged out in headband and fur cape, Presta befriends Leela and a female Time Lord named Rodan, keeper of the transduction barrier. And when, in the final episode, Doctor Who re-enters the phone booth of destiny and departs, Presta is there to wave goodbye.

The only child of prominent Randwick trainer Tommy J Smith, Gai had already graduated from the University of Sydney, taken a walk around the modelling enclosure and appeared in an episode of The Young Doctors. Encouraged in her acting career by British actor James Mason, whose interest in racing had brought him into Tommy’s ambit, she headed to London. But apart from a run in the BBC’s premium sci-fi stakes, she failed to get out of the stalls.

Returning to Sydney, she became an apprentice at her father’s Tulloch Lodge stables and married into the Waterhouse bookmaking dynasty. When husband Robbie was ‘warned off’ as a result of the 1984 Fine Cotton ring-in scandal, his spouse was included in the ban. Showing her mettle, she battled the Australian Jockey Club and won her trainer’s licence in 1992. And when Tommy Smith became ill, he passed Tulloch Lodge on to her. Since then she has shaped some of Australia’s finest horses into champions.

Doctor Who is currently in his eleventh incarnation. Tom Baker became the voice of Little Britain. Despite the best efforts of the tenth Doctor, the Sontarans continue to pose a heavy-gravity threat.