The three weeks it takes to get from Hong Kong to London by train (on a circuitous route) may seem like a long time - and it is a trip you'd want to do for its own sake - but one advantage the journey has over air travel is that it is not likely to be put in jeopardy by an Icelandic volcano. Travelling as a foursome forestalls the greatest inconvenience of transcontinental train travel: sharing a cabin with a stranger who might sit too close, eat cuttlefish snacks or snore. Each compartment on a sleeper train, be it in China, Mongolia or Russia, has four beds and a sliding door, so our nuclear family can settle down, click the lock and interact with Chinese cellphone salesmen, Russian farmers and other fellow travellers in the buffet car and in the corridor, on our terms. First-class two-bed cabins are available with table flowers and, it is rumoured, access to a shower - but all that comes at a price. The line to Beijing is electrified and fast but the view is mostly of rural China: cabbage fields, small houses and sparse, angular trees that look like they've been drawn by a child. There are hardly any trees at all in the vast horizontal views further north, where the train bisects the Gobi Desert and the prairies of Genghis Khan. Here everything seems utterly foreign and Outer Mongolia, as it was known during the Qing dynasty, even sounds a long way from anywhere else. But this journey is really about Russia. We reach it after midnight and, despite the machine guns and uniforms, the border guards are kinder than warnings suggested. They apologise for the disturbance and smilingly compare our children's faces and passports without waking them. The next stop is Irkutsk, by Baikal, a freezing cold and improbably deep lake that contains 20 per cent of the world's fresh water. The lake freezes to a depth of four metres in the winter and in the past, tracks were laid across the ice for the train to steam right over. There's no ice on our visit but a cobalt blue infinity of water that's astonishingly clear and inviting. Legend has it that by dipping a hand into the lake you add a year to your life - brave the waters for a swim and you'll be around for an extra 25 years. I wonder how much you get for a toe, as that is all we manage in water that may not be ice but feels frozen, even in mid-summer. Siberia rolls by at a sedate 50 kilometres an hour and the scenery hardly changes for days: endless forest, rolling hills and the occasional village of brightly decorated wooden houses. This may sound monotonous but it feels adventurous, as we munch our way through Russian sausage and black bread and watch the world's largest country drift past. The line has a marker at every kilometre of the route, so I delight in breaking my family's reverie by telling them, when we are 5,061 kilometres from Moscow, that to the north of the train there is a ruined Cossack fortress among the trees and that the white obelisk at kilometre 3,932 marks the halfway point between Beijing and the Russian capital. They must be relieved when we pull into Yekaterinburg. Most Trans-Siberian travellers complete the Irkutsk-to-Moscow journey in one haul but 70 hours non-stop with a 10- and eight-year-old would've meant a lot of games of I Spy, so we decided to break the journey halfway. Yekaterinburg played an important role in the Russian Revolution; Tsar Nicholas II and his family were murdered here, in the basement of a house. The house is gone but, in post-communist Russia, the tsar has been raised to sainthood and the enormous gold-domed Church on Blood in Honour of All Saints Resplendent in the Russian Land has been built on the spot where the murders took place. The city feels modern and vibrant, with summer pavement cafes along the River Iset and the town-centre statue of Lenin now a backdrop to family picnics and skateboarders. Its wide avenues and 19th-century buildings feel like a first taste of Europe and appropriately so; the signpost that marks the end of Asia is only 10 kilometres west of the city. Back on the train, the marker posts reveal Moscow is a mere 1,816 kilometres and two time zones away. This part of the trip is defined by many excursions to the dining car, each requiring an increasingly desperate attempt to refuse offers of vodka from the free-spirited Russians in residence. Arriving at Yaroslavl Station is a momentous event, partly because here there are buildings and crowds after so many miles without either, but mostly because this is Moscow, one of the world's great cities. Red Square is a must, of course, a cobbled expanse flanked by the Kremlin, the 19th-century Gum (pronounced 'goom') department store and St Basil's Cathedral. We stroll along the Arbat and through Gorky Park, as well, but all too soon we are back on tracks. The journey to St Petersburg is made on the Krasnaya Strela, or Red Arrow, service. The train dates from 1931 and is the most luxurious of our trip. The provodnika, the onboard stewardess, brings us golubtsy - cabbage rolls stuffed with meat - and Georgian beer and draws the lacy curtains on the darkness outside as we curl up under crisp white sheets. St Petersburg is 1,050 kilometres and 300 years away from Moscow. Peter the Great established the Russian capital here in 1712 and the city became a showcase for neoclassical architecture. The boggy terrain along the Neva River that bisects the city saved St Petersburg from the excesses of Soviet brutalist architecture and the communist party had to be content with merely renaming the place Leningrad. Entering St Petersburg is like stepping back in time. Cannon are fired from the Peter and Paul Fortress on the riverside every day at noon, bells ring out from the massive St Isaac's Cathedral, the Church of the Saviour on Spilled Blood and dozens of others across the city. Picnickers lunch beneath bronze statues of Catherine the Great and locals pass fountains in the Summer Garden on the way home from a ballet or opera at the Mariinsky Theatre. Trans-Siberian travellers usually end their journey in Moscow or St Petersburg and board a flight home. We are doing this trip properly, though, and board our next train at Vitebsk Station heading for Minsk, Berlin, Germany and Paris, France, then under the water to London. In Minsk, the capital of Belarus, the streets are dominated by massive Stalinist architecture and tourist sites are few but it's a clean and friendly place. We spend a day here riding dodgems in the park and visiting the circus, where we watch uncomfortably as a man dances with a great, lumbering, shaggy brown bear. The border procedures as we enter Poland are made more protracted by the changing of the train's wheels. Western Europe is on a different gauge to Russia and the children squeal as the whole carriage is winched into the air to facilitate the change while a soldier with a huge walrus moustache checks our papers. Berlin Hautbahnhof, or Central Station, is a modern cathedral of steel and glass and an appropriate gateway to the city beyond. Berlin is fabulously hip and feels uncluttered and unhurried; we hire bikes and ride through the huge Tiergarten, whose wooded glades and lakes make the centre of the city feel further away than the 10-minute walk it is. The Reichstag, the seat of the German parliament, has been redesigned and rebuilt by architect Norman Foster and the infamous barrier that once divided the city has been preserved in parts so that it can be a celebration of the freedom the city now enjoys. A piece of prime real estate right next to the Brandenburg Gate has been given over to a Holocaust memorial of 2,711 concrete blocks spread across a field like some abstract cemetery. And then Paris is just Paris. How can anyone fail to fall in love with the city of boulevards and parks, the Champs-Elysees and the Arc de Triomphe? In the morning we gape at Caravaggios and the Mona Lisa in the Louvre. We eat lunch in an art nouveau bistro and in the evening sit by the River Seine, drinking hot chocolate and watching the view erupt in myriad lights on the Eiffel Tower. The next day we board the Eurostar at Gare du Nord loaded with French camembert and red wine for what is the final leg of an epic trip. Predictably, it is raining in London; we pack away our playing cards and books, and are already missing the stations and buffet cars, and the clickety-clack swaying of a train. But at least we are here - and we don't have jet lag.