'You said this bit would be flat!" My nine-year-old son is unimpressed with my map reading. That morning we'd pushed the bikes up a mile-long 1-in-8 road to get to the High Peak Trail. "It used to be a railway," I'd told him, "and trains don't go uphill." But the trucks on what was the Cromford and High Peak Railway had done exactly that. At the top of our unexpected hill we found the house-sized static steam engine that used to haul them up.
Of course, you expect hills in the Peak District. Unfold any map of the area and the contour lines cluster together like the whorls on a fingerprint. Scattered around on the roads are those tell-tale "V" signs: one "V" for 1 in 7 (Very hard), two for 1 in 5 (Very, Very hard). And as all the old-stone towns are in the valleys, sooner or later you'll hit a hard climb if you travel between. Racing cyclists relish these roads, but if you're cycling with children and luggage, as we were, you'll walk.
On quiet roads it's more leisurely than it sounds; we took the time to chat, eat sweets, admire the views, watch the kestrel hovering. It's only the Peak District's heavily trafficked roads - the As and Bs - that are unpleasant.
Yet you can escape both traffic and hills, courtesy of old converted train lines that haven't seen track or trains for decades. The 17-mile High Peak Trail is just one of them, and other than the steep climb at the end - it was built as a transport link to cross the high ground between two canals either side of the Pennines - its cuttings and embankments keep it flat. It joins the Tissington Trail, a 13-mile path on the site of the old Ashbourne-Buxton railway line, which is less exposed and flatter still. Only a few miles further on is the best and easiest of the lot: the Manifold Way, a pan-flat eight-mile path along the bottom of a stunning limestone valley, once the home of the Leek and Manifold Light Railway.
Foot and mouth disease shut the trails, but they're open again now, offering cyclists and walkers a network of nearly 40 off-road miles through some of Britain's best scenery. Yet the gradients are so easy that a five-year-old could ride most of it; we saw many children doing just that, some still with stabilisers.
Bike-hire centres with adjacent car parks sit on all the trails, so you don't have to pedal (or push) your own bikes to get there. If you don't think your children can manage the mileage - and going west on the 1,000ft High Peak Trail into the teeth of the prevailing wind, it can be hard - you can hire a variety of child-carrying conveyances. There are childseats for toddlers, two-seater trailers for teenies or siblings, and trailerbikes for bigger kids. A trailerbike is basically half a child's bike plus a tow bar, which links to the adult bike to form an articulating tandem. If your child gets tired, you can pull him along.
We met cyclists every mile or two, and just once a stream of huffing orienteers. Otherwise we had the lush, rolling landscape of the Derbyshire Dales to ourselves. The trail twisted and turned to keep its height, through lichen-crusted rock cuttings and over old stone embankments that looked like Hadrian's Wall. Lambs filled the high fields while finches flitted between hedges.
The High Peak Trail cuts across open countryside with no halts en route. Once you leave Middleton Top, you have a dozen miles or so to get to Hartington or Parsley Hay. In contrast, the Tissington Trail links villages, and the Manifold Way has a couple of tea shops along the way, making both of them easier for families to complete.
We, never had any problems - other than a two-mile hill on a busy road we shouldn't have been on, coming out of Chesterfield - but whenever you're riding with children you need to look to their needs. Take plenty of sugary snacks. Not only will they keep morale high, they'll provide instant energy to keep little legs turning. Unless it's genuinely hot, children will often need one layer of clothes more than you because they won't generate as much heat (they won't be working as hard!).
Keen fathers need to remember that they're not in the Tour de Wherever, either. The cycling is a means to an end. Enjoy the landscape and the nearby attractions - there's everything from theme parks to standing stones in the Peak District, all close together.
Don't ride all day. When in doubt, stop for some cake and think it through rather than press on. Children are resilient,but they won't always thank you for dragging them 15 miles further. If you're cycling point-to-point, rather than from a fixed base, this may mean revising your travel plans. We halved our first-day's mileage after struggling on that long climb.
The main reason we could do this is that we were staying at Youth Hostels. Wherever there's great scenery in Britain, there are Youth Hostels. They're cheap; they always have showers and a bike store; and they tend to be walkers' distances apart. A walker can't cover as much ground as even the slowest family cyclist, so you're always near enough to the next hostel.
Youth Hostels today have cast off their cagoule and Kendal Mint Cake image. They're like Travel Lodges for walkers and cyclists, but Travel Lodges with soul, set in fantastic surroundings. Hartington Hall, where we stayed, is a 17th-century manor house with oak panelling on the walls. Bonnie Prince Charlie stayed there, apparently. Even better, for most of our party, they had table football and air hockey.
Next day, we rode down the Manifold Way and were suitably agog at Thor's Cave: a huge limestone hole in the hillside that's been home to man and animal for 50,000 years; mammoth and giant-bear bones have been found nearby. On a longer holiday we'd have continued on by road to Alton Towers, which is less than 10 miles from the trail's end at Waterhouses. We'd have stayed at Ilam, too, and returned to Hartington on the Tissington Trail.
As it was, we retraced the High Peak Trail to Matlock where we took a cable car up to the Heights of Abraham. At the top, the old lead mines have been turned into show caves. They've been show caves since Victorian times, when well-heeled ladies and gents were lowered down in baskets, sold quick-burning candles for a penny, then charged another penny to be rescued and hauled to the surface when their candles burned out. Today, electric lighting lines the route and the guides aren't so opportunistic.
The Victorians would have toured by train, of course; and it's thanks to their industry that we've now got such splendid tracks to cycle on. While you can cycle by road in the Peak District, you're best on the little wiggly yellow roads - with a light load. It's a bit hilly, you know.
Way to go
Getting there: By road, Matlock is 20 minutes from the M1 (J28/29). Hartington is 9 miles from Buxton, where the 442 bus leaves for both Ashbourne and Hartington. Matlock and Buxton are the closest railway stations, but if you want to take your own bikes you're restricted to two - and no tandems - on these services. A trailerbike counts as a bike. Matlock (change at Derby) is served by Central Trains (0121-6541200, www.centraltrains.co.uk). Reservations are free. Buxton (change at Manchester Piccadilly) is served by First North Western (0870 2412305, www.firstnorthwestern.co.uk): bikes are free, but there are only two spaces allocated on a first-come, first-serve basis. If you want to transport more bikes - or a tandem - Chesterfield and Stoke-on-Trent are the closest mainline stations. Chesterfield is served by Midland Mainline (0845 7125678, www.midlandmainline.co.uk) and Virgin Trains (08457 2223333, www.virgintrains.co.uk), while Stoke is served by Virgin Trains. Both services typically carry four bikes, with £3 compulsory reservations per bike.
Where to stay: A dormitory bed in a Youth Hostel costs an average of £10 per adult or £6.90 for under-18s. Separate family rooms are available at larger hostels, costing around £40. To stay at a Youth Hostel you must be a member, which costs £25 per year for a family. To join, call 0870 8708808, www.yha.org.uk.
Maps: Ordnance Survey Landranger 119, Ordnance Survey Outdoor Leisure 24, Goldeneye Peak District Cycling Routes.
Cycle hire: Bikes can be hired from: Middleton Top (01629 823204), Parsley Hay (01298 84493), Ashbourne (01335 343156) and Waterhouses (01538 308609). Mountain bikes cost £7 for three hours, or £10 all day. Trailerbikes, kids' bikes and child trailers cost £5.50 for three hours or £7 all day. More details at www.peakdistrict.org.
Other family attractions: Alton Towers (0870 5204060, www.altontowers.com), Gulliver's Kingdom (01629 57100, www.gulliversfun.co.uk), Heights of Abraham (01629 582365), Poole's Cavern (01298 26978, www.poolescavern.co.uk ), Carsington Water (0121- 722 4339), Chatsworth House (01246 582204, www.chatsworth-house.co.uk).