Major Peake and his two crew companions, a Russian and an American, started their space flight at the Baikonur Cosmodrome, from where Yuri Gagarin began his historic journey in 1961.
They are travelling in a tiny Soyuz TMA-19 space capsule on top of the rocket and it will take them just eight minutes and 48 seconds to reach orbit.
The capsule is expected to dock at the space station at tea time. From there, Major Peake wil conduct experiments and carry out repairs and educational activities for children.
Britons in space
Previous “Britons in space” have either been US citizens or had dual citizenship, or been on privately funded or sponsored trips, whereas Major Peake is employed as a professional astronaut by the European Space Agency.
Helen Sharman became the first Briton in space in 1991. She visited the Mir space station as part of a venture involving the Russian government and British business.
Major Peake, a former helicopter pilot, will be away from his wife Rebecca and two sons for six months. One of the boys, four-year-old Oliver, said simply before blast-off: “I want to go with Daddy.”
Major Peake, 43, and his crew received a blessing from a priest before they left for the rocket.
By tradition, as they travel to the launch pad by bus, crew members jump off to urinate on the wheels.
Although this has never been witnessed by anyone outside an inner circle of astronauts, the tradition is said to have been started by Gagarin when he became the first man in space.