Eddie Grapper is the Sherpa Tenzing of the O2. He's a mountaineer and climber and he's got the beard to prove it. He used to work in advertising but tired of coming up with pithy straplines and decided to devote the rest of his life to craggy peaks, perilous ledges – and managing Up at the O2.

"I'll be honest," I tell him, staring upwards, "all I know about climbing is based on watching Touching the Void and reading The Ascent of Rum Doodle. And in both cases, climbing does not end well."

Eddie nods sagely. "Well," he proffers, "we've all climbed the wrong mountain."

I stare up towards the vastness of the O2. Am I about to climb the "wrong mountain"?

Up at the O2 opened this summer. It's a continuous walkway that takes you over the roof of the old Millennium Dome. The highest I've ever dared climb was a four-foot stepladder and that ended in tears.

"Climbing," Eddie tells me, "is about the intangible and the ineffable. It's about a connection with your environment. You need a spirit of adventure."

"I've got that," I chip in.

"A willingness to explore new things."

"Check."

"You need to want to see what the world looks like from the top of something."

"Ummm."

"And you need a tremendous amount of physical strength."

I blink. "Eddie," I confess, "I have the upper body strength of a daddy-longlegs. And I hate heights."

He stares back at me. "We got a wheelchair up there this morning. We get everyone up and over, whatever their fitness level. I've had pensioners in their 80s do it. You'll be fine."

This challenge isn't quite what I've been expecting. I've spent the past few days fretting as to how I am going to grapple my way up the side of a building, but the setup is ingenious. I'm kitted into a jumpsuit, snapped into a safety harness and then, after a short climb up a perfectly normal set of stairs, find myself at base camp, the starting point of the climb.

"Vertigo can kick in," I'm told. "But trust in your safety harness. The worst that can happen to you is that you fall to your knees. And you will always be the same distance above the roof. That can be a comfort."

I stare upwards. The walkway is like a stretched, ridged trampoline with a wire running up its centre. It's very steep but the good news is that after the first 20m, the walkway gradually flattens out in increments until you hit the centre. All the same, the emotion I'm feeling isn't comfort. It's more gnarled terror mixed with the fear of a suddenly loose bowel.

I'm clipped onto the wire and told that I must, at all times, keep one hand on my safety clip. It has to remain in the "smiley face" position in order for me to move and, from the off, I find this quite tricky, mostly because all I want to do is hold on to the central wire with both hands and make noises like a wounded goose.

However, the fact I have to concentrate so hard on maintaining the smiley face clip position means I have no time to think about how I am shimmying up the side of a very large building and before I know it, I've reached the first peak.

"Don't forget to look around," says our guide, Tom, who is lovely.

I can't quite do that yet but I'm determined to conquer my revolting fear of heights and, at some point, take both hands off the wire and the clip and do a proper Chris Bonington hands-on-hips grin.

The climb, I'm discovering, is more akin to a fairly strenuous walk. The early upwards sections are tough on the calves, but the higher we go, the easier it becomes. There's a certain amount of bounce to the walkway that takes a little getting used to and I wish I'd worn a slightly sturdier shoe, but as we approach the summit, dare I say it, I am actually enjoying myself.

There's a large observation deck at the top and I am overwhelmed with a sense of achievement. "I have climbed atop," I cry. "I have stood aloft and I can declare I was here!"

"Yes, you can," says Tom, smiling.

I have conquered the grand peak of the O2 and if I can do it, so can you. All I have to do is get back down …

• The trip was provided by Up at the O2 (0844 856 0202, theo2.co.uk/upattheo2). Participants must be aged over 10, be taller than 1.2m and weigh less than 21 stones. Tickets from £22pp

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