Now if you'd said the Bure to Messrs Lewis and Clark, they would have been nonplussed. In the 19th century this 50-mile waterway through the Norfolk Broads was a well-known thoroughfare busy with wherries, the black-sailed Norfolk cargo boats. There was a system of locks and a long-established trade in coal, flour and timber. In 1912, however, came a great flood that would finish this cosy arrangement forever: locks and bridges were washed away, boats wrecked and sunk. When local people assessed the damage, they found that only one boat – the Zulu – had survived and the repair costs for the entire network were prohibitive. The railways were eager to take the trade away and so they did. The river Bure was largely abandoned by man.

For a century it lay untouched, its upper reaches unexplored and inaccessible. It became a wild and primeval place. Tribes of otters, deer, pike and dragonflies sneaked back in and settled down. Lewis and Clark would have been amazed and then intrigued. They would have stared at that blank space on the map north of Wroxham and the A1151. They would have notified the Royal Geographical Society. Finally, they would have mounted An Expedition.

Our starting point is upstream at Aylsham, once the last navigable settlement on the Bure, where we meet Mark Wilkinson, founder of the Canoe Man organisation, who has foolishly agreed to allow us to be the pioneers on his tipi trail. Mark watches as we fumble, stumble and wobble on to two of his rather smart green Canadian canoes. Niall (15) and Maddy (8) are trying to whack one another with paddles. Sophie (21+) screeches when one foot gets wet. Caitlin (21) is already trying her hand at it, burying the nose of a canoe in the opposite bank.

I can sense that Mark thinks I've lost control of my team. Last time I was here, a few years ago, he took me on a very different experience: a wildcamping survivalist paddle. And although this is family-friendly trip, luxurious in comparison, I've clearly remembered no basic canoe skills. "Just remember the rear paddler does the steering, not the front. You'll be fine."

Everyone is in a state of high excitement, which is only slightly dented when we run aground almost immediately. In places the water in the side channel where we have embarked is barely a hand's breadth deep. We all get out and push into deeper water. The canoes swing around under some low branches. Maddy gets caught on one. The canoe tilts, breaks free and rams into the bank. We proceed thus, banging and pranging for a while before the river itself, perhaps in a fit of exasperation, turns our bows decisively downstream and starts to sweep us firmly towards our final objective: the town of Horning, three days' paddling hence.

The sunlight is bursting through the spring foliage, the ducks are dabbling in the shallows and frogs are croaking with glee – probably at our clumsiness. It feels like that moment in The Wind in the Willows when Mole gets his first taste of "messing about in boats" and falls head over heels in love with the whole business.

Our first tipi is probably the hardest to find, tucked in a field within comfortable reach of The Goat Inn in the hamlet of Skeyton. This is not luxurious camping, but it is simply comfortable and well-organised. A couple of large plastic tubs hold food for the morning (we eat at the pub that night); our beds are sleeping bags on futons. Outside is a campfire all laid out ready. We just strike a match.

Had we had Lewis and Clark along, I suppose we'd have been at our paddles at dawn ready for a 12-hour. Instead we drift together in front of a rekindled fire at nine and try to demolish the breakfast depot left by Mark and his men. By ten, with lunch hamper securely stowed, we take once again to the water, proceeding in a rather leisurely manner downstream. The paddling is easy, the water pure and clear. All around is green tranquility on what for me is the loveliest section of the Bure – the bit above Coltishall Lock where motorboats cannot go.

I am looking forward to meeting the motorboat people in the same way that Lewis and Clark looked forward to encountering the Teton Sioux: with trepidation. The canoe skills of some of our group are such that they need the whole river to themselves. Maddy is threatening to overturn hers, "to see what it's like". Niall promises to oblige her, without warning. Caitlin is still zigzagging along, gently bumping into alternate banks at regular intervals.

Our first sight of motorboats comes as we lift our craft over the porterage at Coltishall Lock. They are all tied up and looking peaceful. Then we spot our tipi on the lawn of the Norfolk Mead Hotel. Don Fleming, the affable owner, comes over to welcome us – pioneers on the tipi trail – and mentions that his hotel has a bar. Sophie and I slope off there later, leaving the rest running around the lawns. Don and his wife, Jill, have lived here on the borders of motorboat territory for many years, maintaining a sense of humour and a delightfully unstuffy country house hotel.

Dawn is misty and filled with the warning calls of otters. We set out again, now showing encouraging signs of competence, nosing our way through tendrils of vapour, wondering what to expect. Niall and Maddy have stopped squabbling and are proceeding in a straight(ish) line. Sophie, Caitlin and I are loaded in the other canoe. Cattle and horses watch our progress. In sections under trees, the light is sombre – sufficiently dark for a bat to flit across our path in the middle of the day. All is quiet. We pull over for a picnic a mile north of Wroxham and swim in the river.

I am in the water when it happens. A moorhen on her nest gives a warning cluck. I swing around and spot a squat low hull approaching from Wroxham in a cloud of blue fumes. There's not even time to get back to the shore before it's beside me, throwing up a wake that sends the moorhen flapping to safety. The boat's chief doesn't see me, but I see him, a thin man staring fixedly ahead and clinging tightly to the ship's wheel. His face reminds me of commuters stuck in traffic on the M25. Behind him, lying on the poop deck, is his vast consort, baring most of her body – I've heard that these motorboat people worship the sun. In a minute, however, they are out of sight around the bend and I relax and return to our lunch camp. The moorhen hops back into her nest and settles down on her clutch of three eggs.

Back in 1805, when dealing with the Sioux, Lewis and Clarke tried gifts of beads, tobacco and shiny metal weaponry, but I decide against this. When we embark once more, I tell the crew to stick to "Morning!" or "That bacon smells good." The strategy works well initially, but as we head through Wroxham our nerves begin to fray. There are motorboats to the right of us, motorboats to the left. We are all well aware that at any moment the mood can change and we are heavily outnumbered. Motorboat people have proliferated in the warm pubs and landings around Wroxham and now consider it their private reservation. Fed on fossil fuels, meat sandwiches and ice cream, they view canoeists with suspicion – after all we paddlers are silent (except Maddy), odourless (almost) and do not destroy riverbanks (except every 20m in Caitlin's case).

We're almost through the settlement when disaster strikes. A boatload of drunken tribesmen send their cruiser veering wildly around the river while they wave shirts in the air and yell their traditional war cries: "Whoaar!" and "Yer!" and even the spine-chilling "Narrr!" They then grab some oars and begin whacking water at us. I beg Niall, our teenage interpreter, to translate, but he doesn't speak their dialect. The situation is deteriorating fast. I have no option but to shoot two of them with a malevolent stare. They roar off, hooting with laughter.

Crisis over, we relax and even begin to enjoy observing this unusual and colourful tribe in its natural habitat. Elegant thatched homes line the riverbank, with huge motorcruisers at private landings. Some tribesmen wave to us in a friendly manner from their sun-worship decking, and one even shouts at Maddy in passable English, "Paddle harder, Number One!"

An hour later we turn off the river and into Wroxham Broad, the territory of a different people – the sailing fraternity – but we are under strict instructions from Mark not to provoke them, and to keep respectfully to the margins of the lake. Quite why this tribe and the motorboat people so dominate the area while canoeists are expected to creep around on the fringes is a question that must be addressed to the Great White Queen – otherwise known in these parts as the Broads Authority. Finally, with some relief, we spot our tipi on the far side of this great water, its tall white sides just visible among the trees.

Our reward for this tricky passage is the most idyllic campsite of the lot. Secluded in woodland and surrounded by glades of flowers, we are actually in someone's back garden – the grounds of a former hotel. After dark we even receive a visit from a friendly local, John Brown, who comes to see how we are surviving. John turns out to be a superb singer and our last night is a memorable one: campfire under the stars and John's brand of soulful blues.

Our last morning is all too short: a few hours' paddle and we are in Horning, a quaint settlement with a lovely B&B, The Moorhen, where, back in civilisation, we shower and have lunch. The expedition is over, the Bure conquered. We await our medals from the Royal Geographical Society.

• Canoes from The Canoe Man (0845 496 9177, thecanoeman.com) cost from £50 a day. Tipis for up to five people cost from £99 a night, including equipment and luggage transfer. The Moorhen (01692 631444, themoorhenhorning.co.uk) has doubles from £75 B&B. The Goat Inn (01692 538600, skeytongoatinn.co.uk) charges £10 a night for a tent and two people, and mains in its restaurant cost from £9.50. At the Norfolk Mead Hotel (01603 737531, norfolkmead.co.uk) doubles cost from £100 B&B, main dishes in its restaurant from £15