Britain at its best: This city has the Exe Factor, with a stunning cathedral and Roman remains

There are bones at the end of the tunnel. Just as I think I can make out the shape of a human skull, the torch blinks out, plunging me into blackness. Something booms above me. I crouch lower.

‘It’s probably a car driving past John Lewis,’ says John, our guide, from the darkness.

He turns his torch back on and urges our group to follow him deeper into Exeter’s bizarre Underground Passages complex, built in the 14th century to provide water to what was, at the time, emerging as one of the biggest cities in the country.

John reassures me that the skull I spotted is a replica, placed there as a reminder of the many who died during this tunnel’s construction, which coincided with the outbreak of the Black Death.

After 20 minutes more hunch-backed walking, I ascend stairs into sunlight. I’m appreciative of Exeter’s subterranean history, but ready for above-ground cheer.

And it’s here in abundance, especially in the Southernhay House Hotel, just a few minutes’ walk from the River Exe and the gargantuan cathedral in the centre (which features the longest uninterrupted Gothic ceiling in the world).

Exeter is compact enough for walking, and it’s the kind of unstuffy city that wears its rich history lightly.

It’s also a place that rewards aimless wandering around its eclectic hotchpotch of Tudor shopfronts, Roman walls, narrow alleyways packed with quirky stores and a surprisingly wide-ranging restaurant scene.

I meet David, one of the legion of Red Coats who lead free walking tours of the city.

Exeter’s cathedral features the world’s longest uninterrupted Gothic ceiling

At the end of our 80-minute stroll around Roman remains and the ditches of William the Conqueror’s castle, we reach the Royal Albert Memorial Museum, a treasury of artefacts. This is where, thanks to huge-scale model maps and grainy news footage, I learn how Exeter attracted some ‘bad’ tourism.

As revenge for the Allied bombing of Lubeck (a beautiful city that was targeted in a bid to lower German morale), copies of the popular Baedeker travel guides were purchased by the Luftwaffe high command to identify pretty towns where the destruction of historic sites would cause the most sorrow.

Exeter was the first target of what became known as the Baedeker Raids, obliterating the city’s library and much of the centre and killing hundreds.

Heavy cloud cover and the RAF prevented more substantial damage. Though, as I discover, this is a city that likes to keep some of its treasures well hidden.

I spot a glass case brimming with coins — this is the Seaton Down Hoard, an astonishing collection of more than 22,000 Roman coins discovered in a south Devon field in 2013. The coins are a perfect symbol for Exeter: modest and un-showy, but surprisingly rich and bountiful, both above and below ground.