I am standing in the car park outside the Top Gear studio hangar in Dunsfold Park in Surrey, trying to poke my hand far enough up the inside of my crash helmet to straighten my ears. A white Porsche GT3 idles throatily beside me, passenger door open. Behind the wheel is the Stig, visor down, looking impassive and a little menacing. I swallow hard, climb in and shut the door.

"How's it going?" I say. The Stig stares straight ahead, and says nothing.

I know the Stig isn't supposed to talk – that, strictly speaking, he's a role without lines – but in person his silence is still unnerving. Even when you have your picture taken with him, the Stig only responds to the photographer's instructions when they're delivered through an intermediary.

We drive a short distance to the edge of the Top Gear track, about 50 metres past the starting line. The sun beats down on the tarmac, sending up shimmering waves of heat so thick they cast shadows.

"Nice day for it," I say. The Stig stares straight ahead, and says nothing. We can't pull out yet, because there's another car on the track – we have to wait our turn. After a few moments, the unnerving silence becomes merely awkward. Imagine waiting at a bus stop with the Ghost of Christmas Yet to Come.

By this point I've already been at the track for several hours, taking in the soon-to-be-launched Top Gear Track Experience, an attraction created by BBC Worldwide in partnership with a company called Brandscape Group ("A global brand consultancy specialising in design and operation of experiential and advocacy programmes, brand experience centres and brand communications," says its website).

Improbable as it sounds, from the end of August, ordinary punters will be able to come to the Top Gear HQ, poke around the studio, sit beside the Stig while he does a fast lap, and even drive a Reasonably Priced Car round the Top Gear track at speed. It adds up to an expensive day out – the Star in a Reasonably Priced Car experience alone will set you back £175 – but I'm here for the press day, so it's all free for me, a bunch of giddy motoring journalists and our kids (there are attractions, including driving, for the under-17s).

I can't help worrying that much of the experience will be wasted on me. I'm not a petrolhead. I've never quite understood what is meant by the term "understeer". My idea of an extreme motoring challenge involves a hire car and an Italian airport access road. I've already been driving for two hours to get here, and along the way I had to perform several difficult and dangerous manoeuvres just to extricate myself from Guildford. I'm quite keen to stretch my legs.

My first experience, fortunately, is not on the track, but on an off-road course. I'm at the wheel of a Land Rover Defender 110, a beast of a vehicle. We're moving at a stately pace – it's difficult to top 12mph in third gear – over a series of impassable looking mounds, banks and ruts. The Defender has the turning radius of a bouncy castle, but once I get the hang of it, it's tremendous fun to drive. Neil, my off-road tutor, guides me between two poles, one of which has a cutout of Jeremy Clarkson's head stuck on it.

"A bit more to the right," he says.

"You want me to run over Clarkson's head?" I say.

"I'd be disappointed if you didn't," says Neil. I miss.

He then directs me up a daunting incline, and tells me to pause at the top. As we crest the hill, I hear the sound of machine-gun fire. This is not just a sound effect: when I turn my head in the direction of the noise, I see a guy in a tank shooting at me. Neil pulls out something that looks like an automatic weapon – for a moment I think he's going to return fire – but it turns out he's only checking the hits on the laser targets glued to the outside of the vehicle.

"Unfortunately, it was a catastrophic kill," he says. I was following your orders, I think. You told me to stop here.

Before I return to the track to face the Star in a Reasonably Priced Car challenge, I'm given a go in a simulator, essentially a Top Gear PS3 game. I crash twice, irrevocably – a man has to come and reset the machine for me.

Nathan, my racing coach, takes me through a big map of the Top Gear track. If you're like me, you will have watched the show enough times to know the names of its features – Gambon, Hammerhead, Follow Through – without necessarily knowing what they correspond to. I find the figure-of-eight route confusing, and eerily reminiscent of Guildford's one-way system. By the end of the lecture, I'm no longer worried about crashing, I'm worried about getting lost.

Luckily, Nathan stays with me, in the passenger seat of my liveried Kia C'eed. As we reach the track from a side road, the pit of my stomach rings hollow – it's like taking a wrong turn at the airport and suddenly finding yourself on the runway. Nathan points me in the direction of the starting line. I put my right indicator on, and pull out.

The first lap is practice. Nathan points out the optimal line, suggests appropriate gear changes and tells me when to brake and when to floor it. Then we pull up to the starting line, where a man in a white coat is holding an enormous union jack. He waves the flag, and we're off.

Getting the go-ahead from a man with a union jack. Photograph: David Levene

Let's just say I overcame a lot on my second lap: the sense that screeching wheels indicates something very bad; the urge to brake when I should be accelerating; the impulse to scream when approaching a wall of tyres at speed without quite knowing which side of them I'm meant to end up on. My time was dismal – 2min 15sec – not quite the worst of the day, but nearly. However, I came to Dunsfold Park expecting a hot and slightly dismal few hours at the track, and in the end I was thrilled – childishly, shamelessly, properly thrilled – by it all. I immediately wanted another go – if only to post a time faster than John Prescott's – but a queue had built up behind me. My next lap will cost me £175.

Waiting at the trackside later that afternoon, the Stig and I still haven't found a way to break the ice. I feel compelled to speak – I want to ask him if he knows a shortcut to get to the A3 – but he suddenly reaches out a glove and selects a Daft Punk track on the CD player. He turns it up so as to prevent the possibility of further chat, and roars out on to the track. I had always assumed that this would be the most terrifying part of day, but as the Stig threads his way round a turn I now know to be called Chicago, I find that I am observing his technique for future reference. I'm going to show Guildford a thing or two on the way home.