It's a summer's day in Donegal and it's raining. Quelle surprise! I'm sitting in a minibus full of young overseas backpackers, who are on a six-day exploration of Ireland with Tir na nOg Tours.

It's the third day of the tour, which originates in Dublin and then goes on to Carlingford, Belfast, the Antrim coastline, Derry, Donegal, Sligo, Westport and Galway. Liam Devine, the Belfastborn guide, has just driven high up the narrow, winding road that leads to the stone fort of Griannan an Ailleach.

The car park is deserted. Lough Swilly, the Fanad and Inishowen peninsulas are shadows of their real selves. Fog swirls around the bus. Rain pelts at the windows. Liam has just given us a short talk about the Griannan and the effort of motivation to go out and see it in the pouring rain is beginning; people gathering their jackets and putting up hoods.

A car draws up beside us. Liam glances out the window. In fact, he almost falls out the window, such is the effect that the driver of this car has on him.

"That's John Hume!" he says. Amazement is not an adequate description of the look on Liam's face. "John who?" is the general chorus from the bus. Liam has opened the window and is hailing John Hume, for it is indeed him, out for a jaunt with his American visitors.

Blue and white golf umbrella in hand, John Hume comes aboard. "You're very welcome to Ireland," he says, beaming away. "Sorry about the weather!" He gives us a little impromptu spiel about the Griannan and then he asks where everyone is from. "My friends are from California," he tells us, waving the golf umbrella in the direction of his car. "Are there any Americans aboard?"

There is one American on the minibus. Angelique Boersma gets to her feet. "I'm from California too," she says excitedly. "From Orange County!" This is day four of the Siege of Drumcree. It is one of those extraordinary moments which makes Ireland such a sublimely surreal place to travel in.

Then John Hume gets back into his car. Himself and his party wave at us. We wave back at them. Then they're gone.

"Who was that guy?" everyone is asking. Liam is still staring out the window. "That guy," he says, "is responsible for the Peace Process."

"Cool," someone says, and then quips, "can you fix for us to meet U2 too?"

Tir na nOg has been operating mini-buses out of Dublin for six years, running no-frills tours both in the North and South, aimed at the 20-30 age range of independent backpackers, who are travelling on limited budgets. The cost for a six-day tour is £169. Accommodation is in hostel dorms, there are "shop stops" every day so that people can buy food to cook that evening, and the route is off-the-beaten-track wherever possible, with local guides giving back-up tours along the way.

There are 21 people on board. Fourteen are Australian, five are New Zealanders and there's one Canadian and one American. There's a rule that whenever there's a stop and people get off the minibus, you must sit in a new seat when you come back, the idea being that you get talking to everyone.

We're heading towards Letterkenny, The Cranberries are playing and a box of Maltesers and packets of biscuits are being passed round the minibus. It's a bit of a squash on board. All the rucksacks are heaped together in the back and there's not a lot of leg room, but nobody seems to mind. There's an atmosphere of cheerful solidarity, and a lot of banter is being exchanged between Liam and his passengers, who refer to him teasingly as "Uncle Liam".

What did they make of their brief time in the North? "I think the Northern Ireland politicians are like those lefty politicians in Australia," offers Marina Damijanic (24). "They seem really embarrassing, what I've seen of them on TV. No, that's not the right word. They seem irrational and opinionated."

"Before I came to Ireland, I used to wonder why people stayed living in Northern Ireland if it was so awful, but now I've been there, I understand that it's home for people who've lived there for generations," says Claire Wiggins (23). "But I wouldn't really have any opinions on what's going on. I don't know enough and I don't live there."

At 61, Betty Mahy from New Zealand is the grande dame backpacker on board. It's the first time she has been overseas and she's travelling alone. "This tour appealed to me because I'm travelling on a budget and it seemed a good way to meet other people. I don't mind that I'm much older than everyone else here. They treat me just the same as they do each other."

"If we'd rented a car, we'd never have been able to see all the places we've seen this cheaply. Petrol alone would cost a bomb," comments Greg Holmes (27) from Sydney. He's been overseas for two years and met his New Zealand girlfriend, Mikayla Park (24), along the way.

Backpacking on a budget has its drawbacks where romance is concerned. "Because the accommodation is in separate dorms, we don't get to sleep together," Mikayla says, her arm around Greg. "We'll be looking forward to getting back to Dublin."

Pulling out of Letterkenny after lunch, Liam warns us: "We're heading towards some of the worst roads in Ireland." Rain is still cross-hatching the windows. He's not exaggerating. After a couple of miles the rucksacks are jumping in the back, jackets and bags of shopping are falling down from the shelves overhead, and everyone is shouting as yet another pothole is negotiated.

We bounce alongside the long silver slice of water that is Lough Finn. The mist is squatting on the mountains. Turns are taken to wipe condensation from the windows. "Did you get good pictures of the police stations in the North?" someone asks. Iarla O'Lionard is playing as the minibus climbs the Glengesh Pass. It's 4 p.m. in the middle of summer, but already the light is dim and grey. There's a photo stop at the top of the pass. A few people huddle together under an umbrella and have a smoke in the rain. By the time we get back on to the bus, we're like a flock of wet sheep.

So what have they been buying by way of souvenirs? "No dust-collecting items," Natasha Goodwin (23) from Sydney reports. "Everyone's bought postcards. Especially ones of Belfast, because they're unusual cards to send. Celtic jewellery. Small portable things that'll fit in a rucksack. We'd all love to buy sweaters if we had the money." Natasha had bought her granny a jar of Irish Whiskey Marmalade in Letterkenny.

Angelique from Orange County pulls her trouser leg up. There's a tiny black shamrock tattooed above her ankle. "I got it done in Dublin. I wanted a permamant reminder of my first trip to Ireland," she says.

At Carrick, Liam stops the bus. "Slieve League, the highest sea cliffs in Europe, are only about 15 minutes' drive from here," he tells us. "But there's no point going. We won't see anything today." There's a sense of resigned disappointment in the bus. "We'll stop for a drink in Killybegs instead," Liam promises. "And when we get to Donegal town, I'll show you the castle."

"Ireland looks very familiar to me," says Isaac Ryan-Groves (21) from Melbourne, over a drink in Killybegs. Karen Beamish (27) from New Zealand agrees with him. "I feel at home here," she says. Isaac has been reading history books about Ireland since he was 15, intrigued by his great-grandmother's roots. "I think there's such a thing as a genetic memory," he suggests. "Maybe that's why the places I'm seeing look so familiar."

Isaac is the only backpacker who recognised John Hume. "Seeing him was like having a connection with history," he says, still marvelling at the coincidence of it. "John Hume getting on our minibus has been the highlight of my whole trip overseas." He looks out the window at the gulls swooping over Killybegs Harbour, and he can't stop grinning.

Next Tuesday: Rosita Boland joins language students as young as nine for a Wicklow whirl.