I’M en route across the famously silvery Tay to Dundee in search of two pieces of remarkable history that have both recently faced an existential threat. One is a ship – but not the one you’re thinking of – and the other is a hulking onshore edifice that ties deep into the fabric of Dundee.

The ship is not the wondrous RSS Discovery. That brilliantly preserved tourist icon does not need travel writers to help keep her future alive. The HMS Unicorn most certainly does. As well as major donors. And you, whether you just want to visit, or can manage a wee contribution.

The Unicorn is in danger as she celebrates her 200th anniversary in a perilous position in Victoria Dock.

Matthew Bellhouse Moran, the Unicorn’s director, explains: “Our beloved Unicorn faces an existential threat in that without action, she could sink and be lost to future generations. That would be a tragedy we are working hard with Project Safe Haven to avoid, but we need help in this challenging journey.”

I head aboard Scotland’s oldest still-floating ship, one of the six oldest in the world. Part of what makes her so unique is that she was never dispatched into active service, never scarred by combat, never sunk, never wrecked. She is still an original. A one-off. I love that you can scramble all over a 46-cannon frigate built in the Royal Naval Dockyard in Chatham in 1824. There are four decks to explore and I get stuck in, stooping my head on some decks to avoid bumping it, as many a Georgian sailor must have.

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Each deck is alive with layers of history. There are tales of marriages formed aboard after she came to Dundee in 1873. I learn too of Adam Duncan, Scotland’s very own Lord Nelson. The Unicorn has been an integral part of Dundee life as a training ship (once renamed the Cressy) then a tourist attraction for 151 years. It’s mindboggling that the Unicorn has been here longer than the landmark Caird Hall and before the city’s Cathedral was consecrated.

Many a British royal has come aboard. Princess Anne is said to be a big fan. But perhaps the most bizarre visitor was the captain of U2326. This German submarine in 1945 became the only submarine ever to be surrendered to a Georgian warship. I’m in good company with my head banging as apparently the German officer cracked his head on its decks too.

I’m intrigued by the name, as I associate unicorns with Scotland. “You’re right,” says Matthew. “There were Unicorn ships in the Scottish Navy until one was captured during the Rough Wooing. The name was kept on – initially perhaps just to spite Scotland, but over the years, it just became another proud Royal Navy name.”

The HMS Unicorn is utterly fascinating and I could scarcely recommend a visit more. One of her problems, though, is that she is shut away east of the centre. RSS Discovery used to be a great complement next door, but now she sits with her new pal, tourist superstar the V&A Dundee, further west along the rapidly transforming waterfront. The Unicorn attracts a fraction of the visitors of Discovery.

Saving the Unicorn is a colossal task – one Matthew describes as “one of Scotland’s biggest engineering projects”. They have already invested in detailed pioneering modelling of the hull to test its robustness and identify weak points in the two-century-old timber. “The solution we’ve come up with is to renovate the East Graving Dock and elevate the Unicorn so we can work on preserving and bringing her back to her best.” They plan on creating an on-shore visitor experience too.

The second iconic attraction that has faced a recent existential threat lies less than a 10-minute walk away. It is the old jute mill, now housing hip Hotel Indigo Dundee. Back in the days when 1000 Dundee-built ships sailed the world’s oceans and traded with its bustling docks, the city famously thrived with jam, jute and journalism.

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In its heyday, the hulking mill was owned by the all-powerful Baxter family. Opened in 1822, it boomed as one of the world’s biggest jute mills. The jute boom ran its course and in recent decades, the building really started to decay, deteriorating into such poor condition it was placed on the register of buildings at risk.

That was when private investment stepped in, aided by a European Union initiative to save buildings of heritage importance. John-Pierre Permutt was one of the investors behind the building’s resurrection as a 102-bedroom hotel: “When we bought the old mill in 2016, it was in danger of being lost forever. That would have been a tragedy. Instead, we’ve saved it and now employ a team of more than 100.”

Operations manager Dirk Bunskoek is proud too of the heritage: “When the Baxters ran the mill, it even conjured up sails for the Cutty Sark. Letting those stories go was not an option and you can see from all the old pictures in the hotel how we proud we are.”

Manny Baber is Hotel Indigo’s general manager. He sees the hotel’s survival and the battle to save the HMS Unicorn as positive signs of Dundee’s recent renaissance: “Seeing this magnificent hotel project and others like the Unicorn is inspiring.”

And I have to agree. These two Dundee historic marvels are inspiring and it’s an ongoing story that we can all – even in a small way – be part of.

For more information, visit hmsunicorn.org.uk and ihg.com/hotelindigo/hotels.