Turmoil in Egypt has triggered a sharp fall in tourist numbers, but it is still safe, and if you go now you'll have its treasures all to yourself

The sun is soft and warm as I write this. It hangs delicately a little way above the westerly line of palms, mango and guava trees. The waves beat a rhythm against the steel hull, ropes creak occasionally as they hold back two massive sails filled by a fresh northerly breeze, a donkey brays from the banks and a bunch of kids call "hello" until I wave. I am not a born sailor, but I am on a dahabiya, a replica of the sort of sailing boat an 18th-century grand tourist would have taken – with en suite bathroom, Wi-Fi and a few other modern comforts added. The wind in Egypt blows from the north, the Nile flows from the south, so we are sailing sedately upstream and although I bow to the inevitable, part of me wishes we might never pull in to land.

Over lunch, the dozen other passengers and myself smile the smile of the smug. The boat is ours in the same way that the Pyramids and Karnak temple had been ours: there were no other foreigners. It is no secret that foreigners are staying away from Egypt, but I have never known it as extreme as this. It occurs to me that there were fewer visitors when we went to the Valley of the Kings on Sunday than there might have been if we had come in 1850. Reasons for this are hard to find.

Last year was a turbulent one for Egyptians, with the downfall of President Mohamed Morsi and his government and the violent dispersal of Muslim Brotherhood demonstrations by Egypt's security services sparking violent protests. But none of the tumult was aimed at foreigners, which was why, even though demonstrations and sporadic anti-military violence continue, the Foreign Office has no objection to our travelling to Cairo, Luxor and the south. But visitors have been nervous since 2011, when former President Hosni Mubarak was forced from office, and they have been slow to return to the capital or along the Nile.

A dahabiya on the Nile. Photograph: Alamy

The situation was made worse a month ago when a jihadist group bombed a bus of Korean tourists in Taba, north Sinai. The Foreign Office has put Taba, Dahab and Nuweiba on the "avoid all travel" list, but Sharm el-Sheikh, the biggest of the Sinai resorts, at the southern tip of the peninsula, is still considered safe to visit, and direct flights are still available. Besides, Taba is several hundred miles from Cairo and the Nile, and the problem there is very different from the stand-off between the military and the Muslim Brotherhood. Staying away from Egypt because of what is happening in Sinai would be similar to avoiding London because of trouble in Belfast, and yet tourist numbers have plummeted.

The extent of this collapse in tourism was apparent the moment I boarded the Egyptair flight in London. Online check-in had made it look as though the flight was full – as it would have been in March four years ago – but the plane was half-empty. Cairo is such a fantastically vibrant city that it can be impossible to gauge the presence of foreigners, but there were only a handful of tourist minibuses at the Pyramids, no other foreigners at the Sphinx and we had the Tutankhamun galleries and the rest of the Egyptian Museum to ourselves.

A line of around 20 armoured vehicles parked ou tside the museum, with a soldier at each gun and watched by men from several police vans wrapped in barbed wire, made me wonder if they knew something that I – and the FCO – did not. The Museum sits on the edge of Tahrir Square, once famous for its traffic jams, now better known for anti-government demonstrations. But the square remained calm, the visit to the museum eerily quiet.

Luxor was just as good – or bad, depending on your point of view – because while an empty Valley of the Kings may be brilliant for those of us who enjoy looking at decorated tombs without being harassed by hordes of day-trippers from the Red Sea, revenue from 20 or so visitors the morning I was there is not enough to pay for the lighting of the tombs, nor to put food in the mouths of the guards and hawkers and their families.

Luxor, too, is almost empty. Photograph: Jean-Pierre Lescourret/Getty Images/Lonely Planet Images

Luxor relies on tourism, so when western governments imposed travel bans last summer, many hotels simply locked their doors: occupancy dropped to 1%. Thanks to the efforts of the energetic and enthusiastic tourism minster, Hisham Zaazou, the ban was lifted last November, but the crowds have not returned. The Luxor corniche used to be infamous for its boat touts and calèche drivers pestering any visitor who went out for a walk. They have now disappeared because there is no one for them to pester. The traders who once made it impossible to walk through Luxor souk no longer harangue you as you pass. "Want to look?" one asked and, when I declined, he simply said, "No problem. Have a nice day."

Which brings me back to the Nile and this second "nice" day afloat. Egypt is as stunning as ever to visit – especially this week as freak rains have just washed the dust of many years off the countryside, leaving the blue sky, the green palm trees, the cream temple walls and the sandstone hills more brilliant than ever. In the morning, we were alone at the tombs and ruined city. In the afternoon, when we stopped at Edfu to see the best-preserved of all Egypt's temples, we expected no crowds. We were expecting no bother, either.

"Are you kidding?" said one of my fellow travellers when I asked if anyone was bothered by security concerns. "I know this situation is bad for Egypt, but it could not be better for you and me." She looked across the empty river where very few boats now run, and watched a heron glide to land on a clump of bulrushes.

There are things happening in Egypt – two presidents are up for trial, most of Sinai is in a mess, an election is expected – but the news that matters for people wanting to visit is good: direct flights to Luxor have resumed, new archaeological discoveries have been made, a replica of Tutankhamun's tomb is due to open next month …

There is no shortage of brilliant things to see in Egypt, just a shortage of people to see them.

• Soliman Travel offers seven nights in a five-star Luxor hotel from £465pp, including flights from Heathrow; and a three-night city break to Cairo, also including flights, from £499pp. Nour el Nil (+20 11 16 55 88 83, nourelnil.com) offers a five-night dahabiya cruise departing from Luxor from €1,100pp, including all meals and excursions