You might describe it as hole-in-the-fence TV: an invitation to spend an hour watching other people build stuff on a vast construction site. Except, in this case, the hole looks straight down.

The Fifteen Billion Pound Railway: The Final Countdown (BBC2) is billed as “the exclusive inside story of the race to complete London’s new underground railway”. This is, in fact, the second series. The first concentrated on the drilling of deep tunnels – 42km of them – but that work has been largely completed. This series began with the final tunnel breakthrough under central London: a giant boring machine burst through a concrete wall, and, after a few minutes, a man in a hi-vis jacket crawled out from between its teeth. “Welcome to Farringdon!” shouted Linda Miller, the Crossrail project manager for the station.

If a documentary about a sprawling engineering project can have a star, it is undoubtedly Miller. She is a former US Army pilot and paratrooper, and an engineer by trade, and she helped to build the launch pad complex at Cape Canaveral. Miller combines boundless enthusiasm for the job with military-style plain speaking. And when she’s trying to get across the scale of her mission, she has a certain way of putting things.

“If you were to take the Shard, which is the tallest skyscraper in Europe right now, and lay it on its side,” she said, “it would fit inside of my Farringdon station. We’re enormous.”

She’s not kidding. The £375m station consists of two eight-storey holes in the ground, connected by a series of tunnels. When they are built, the platforms will be 300 metres long. “What that means in the future,” said Miller, “if you’re stepping off the trains at Farringdon, is you need to know which way you’re going, because if you walk in the wrong direction, you’re gonna be half a kilometre from where you wished you were.”

Her main headache seemed to be one of scheduling: the track layers were heading for her station faster than she could clear a path for them. In the end, an emergency tunnel had to be bored from the surface to give workers safe access. Miller didn’t seem as if she actually considered this, or anything else, a headache. “Every day I bounce out of bed ready to come to work and feel great about it,” she said.

Elsewhere on the line, the new Whitechapel station was being delicately assembled around the old one, to minimise disruption. Down the tunnel a bit, they have another issue: the Barbican’s main concert hall is two and a half storeys below ground level, and therefore just 17 metres above the railway. In this section the track is being laid on springs to keep the noise down.

I confess I find this sort of thing endlessly pleasing. I think it has something to do with the contrast between the enormous ambition of the undertaking and how little is asked of me while watching them go about it. It’s impressive, but it’s also gentle and reassuring, and I can admire the work of those involved without having to leave the house. With its grand engineering and flashy technology, it’s like a Top Gear for public transport enthusiasts. As a Londoner, I even ended up taking a bit of reflected pride in the accomplishment: well done me for not making more of a fuss about all the disruption.

There is obviously an element of propaganda in all this. It’s a tribute to the achievement, not a warts-and-all, behind-the-scenes soap opera. There is talk of danger and things going wrong, but this series is focused on challenges being met, and, anyway, everything we’re seeing happened a year ago – back when the Queen went down to Bond Street to rechristen Crossrail the Elizabeth line, and looking not especially happy about it. Miller’s Shard-long Farringdon station will be nearly finished by now.

Doubtless there will be people who despair at all the expense. At one point, Miller made a direct reference to taxpayers’ money, as if she was conscious that viewers might be wondering if a mere Twelve Billion Pound Railway might have done the trick. But there was also a lot of amazing footage taken by drones flying along tunnels, and the whole thing is quite stirring.

In these dark times, a series like this does a lot to bolster one’s fragile opinion of humanity’s competence. If any alien life forms are monitoring our television, I hope they caught a bit of this along with all the election coverage. “As a species we find you backward, irrational and intellectually inferior,” they will say. “But those tunnel-drilling machines are cool.”