I am clinging to a rope ladder, 20 metres above the ground, in a howling gale. “Now imagine you’ve got no shoes on, never mind a harness and a helmet – and the ship is pitching and rolling,” shouts my instructor. Wow. It’s a miracle that any 19th-century sailor made it home alive. (Many didn’t.)

The Cutty Sark, one of the world’s last surviving tea clippers, is launching a new rig climb experience on Saturday, and I was having a sneak preview. Royal Museums Greenwich has teamed up with Wire & Sky, the adventure company behind the O2 rooftop climb and the London Abseil. Its mission is to give visitors a taste of life at sea and a unique view of London – and no doubt to help recoup the losses incurred during the pandemic.

After getting kitted up under the hull, which is almost entirely original and dates back to 1869, we were led through the ship and up on to the main deck. We were regaled with tales from the ship’s heyday, including the legendary race against a rival clipper, Thermopylae, in 1872, when Captain George Moodie refused to stop for repairs even when the rudder was lost.

History lesson over, it was time to climb. I tried to imagine the poor 14-year-old apprentices being ordered to shin up the ratlines in all weathers – there is a reason most of the 653 men who served on the Cutty Sark did so only once. Even with modern safety equipment, it was a nerve-jangling climb up the rigging to the top platform, 21 metres up. The minimum height requirement is 3ft 9in (1.14 metres), but even at a comparatively lofty 5ft 2in (1.57 metres), I struggled to reach some of the rungs with my feet.

The standard climb ends here, but I had inadvertently signed up for the “rig climb plus”. My harness was unclipped at the front and reattached at the back (crew take care of all the safety aspects), allowing me more freedom of movement. I steeled myself and climbed even higher, gripping the shrouds as I was buffeted by the wind. Then, leaving the relative comfort of the main rigging, I inched my way sideways across the lower topsail yard, with just one rope to stand on and one to grasp on to for dear life. This was daunting, but worth it for the crow’s nest view: the Royal Naval College to starboard, the Thames and Canary Wharf to for’ard and the skyline of central London off to port side.

To descend, I shinned back down the ratlines to the tops platform, where there is a zipline to street level. You simply sit into your harness and step off – again, not an action for the faint-hearted. The zipline itself is a slow, smooth, controlled descent rather than a heart-pumping freefall; a final chance to soak up the view.

Those expecting to climb right to the top of the mainmast, 46.6 metres up, might be disappointed – the highest point of the climb is about half that. But all apart from the most hardened adrenaline junkies will get a thrill; I found it much more challenging than similar attractions such as the O2 climb. Plus, it’s a privilege to get so close to a historic London landmark. Just cross your fingers for calm weather – and be grateful that you’re not in bare feet.

• From £41 adults, £26 children, including general admission to the ship (minimum age 12), rmg.co.uk