But we won’t be straying far from the coast, with its cooling winds. And anyway, we’re after something a little bit different. It’s not just the biking. We’re also interested in seeing how the financial crisis we’ve heard so much about is affecting things on the ground.

The most striking of the abandoned structures we find however has nothing to do with the crisis at all. It’s the remains of an outdoor nightclub which stood at the top of the highest hill overlooking Porto Heli.

Shaped like a castle, it seems to have been built largely of styrofoam blocks, but it’s hard to tell as the whole thing is being slowly reclaimed by nature. “It was abandoned maybe 25 years ago,” says George, our Ocean Elements guide, and it makes for a great backdrop for shots as the sun sinks in the sky.

Most of the riding around Porto Heli is on dirt roads rather than singletrack. While they’re fun to blast around, we’re looking for something a little more challenging as we set off the following day.

A bit of a session on Google Maps suggests that if we head to the end of the peninsula we should be able to find some decent trails, but we spend a frustrating – and fiendishly hot – few hours riding around before we stumble, almost by accident, across a trail worthy of the name.

A nice descent and a hot climb up over a ridge later and we’re cutting off onto a long dirt track that seems to lead directly down to the sea. “It looks like we can ride all the way onto a beach down there” I say to Cal, gesturing excitedly at the satellite image on my phone.

Unfortunately once again my map-reading skills are off – it turns out the trail ends abruptly in a series of limestone cliffs. But it’s nearly 30 degrees and I’m a sweaty mess.

Still, armed with a map from tourist information which shows a plethora of trails that look rideable, we set off boldly for the ridge that runs along the top of the island.

One sweaty hour later, when the trail we are climbing has disappeared completely into thorns and dry brush, I finally concede I may have made another navigational error.

As Cal fixes a puncture (a regular feature of riding through such dry spiky undergrowth) we plan our next assault. Thankfully it’s second time lucky, although the top section of our chosen route is too steep to ride and by the time we’ve hiked the bikes onto the ridge we’re drenched in sweat again.

It’s worth it though. Spetses is basically one big hill, just a few kilometres wide, and the views in either direction are mind-blowing. A dirt track running the entire length of the summit ridge takes us up to a small Orthodox chapel, where we sit in the shade and admire the scenery, gratefully sipping the free water left out for hikers (and bikers).

From here, it’s all downhill (literally) and from the looks of the map there are any number of trails to pick from. The one we choose leads us through pine glades and past another picturesque chapel before we hit a stretch of singletrack several kilometres long that winds down over compacted dirt and exposed rock.

It may be because we’ve found it all by ourselves, or it may be simply the pleasure of descending after a hot morning’s climb, but it feels like one of the most fun trails I’ve ever had the pleasure of riding.

Goat tracks across fields carry us back into the outskirts of town and I’m gagging to do it again. But just as we get to the bottom I get yet another puncture (our fourth of the day!) and we realise we’re out of spare tubes.

“No worries,” says Cal, “we’ll grab some lunch then head to a bike shop and get some spares.” However the lengthy Greek lunch break puts paid to our plans – the shops won’t be open again until 5pm and we have a ferry to catch.

Can You Drink Your Way Out of a Hole?

If Spetses is a world apart, an island of wealth sheltered from the worst of the economic storms, the crisis becomes a lot more obvious in Athens.

It’s not as if we’re stumbling into street protests and the city’s most famous sights, the Parthenon, the Agora and the Odeon, are crawling with foreign visitors, even in the midday sun. But Athens looks and feels like a city that’s down on its luck.

Will things get better, we ask? “Well I didn’t vote because I didn’t like any of the options. But I think the latest deal is good, because hopefully in one year maybe things will start to get better.”

If Demi’s air is one of weary resignation, her colleague Elias is more forthright. Slightly older than Demi, he’s angry.

“I voted no in the referendum [on the latest bailout deal, and the accompanying austerity measures]. Not because of the deal but because no-one can tell me what to do in a democracy. All the foreign politicians were telling us to vote yes but they can’t tell us what to do.”

He’s frustrated by what he sees as the Greek leadership’s refusal to stand up for itself and scared about Germany dictating terms to the rest of the continent. “We have seen from history what Germany can do when it gets too strong…” he says ominously.

But if Elias isn’t particularly fond of Germans, he’s certainly not anti-foreigner. Far from it. In fact the one thing that both he and Demi emphasise is how important it is that tourists keep coming.

Around 20 per cent of Greece’s GDP came from tourism before the 2008 crash. Roughly one in five Greeks worked in a job that depended (directly or indirectly) on foreign visitors. If anything, as the rest of the economy has tanked and tourism has stayed relatively stable, the tourist industry has become proportionally more important.

But when you think about it, why wouldn’t people keep coming? As we’ve discovered, Greece is still an incredible place to visit. Tour operators like Ocean Elements are still doing roaring trade because the mountain biking is good, the beaches are brilliant, the food is incredible and the ouzo is cheap.

Yes the headlines might be bad but as a tourist in places like Spetses, Porto Heli and even Athens, you’re not massively affected. In fact the only thing that’s really changed is that now the locals appreciate you and the money you spend all the more.

With this in mind, I catch Demi’s eye and order another round. It may seem silly, but every little helps. Perhaps, I say to Cal, if enough of us come here on holiday we can get the Greek economy back on track, one beer at a time.

Do It Yourself:

One week at Ocean Elements’ Nautica Bay Hotel in Porto Heli starts at £700 per person including flights, half board and free bike hire.

Ferries and boat taxis to Spetses leave roughly every 20 minutes from Kosta, a 5km ride from Porto Heli.

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