He said it could bring huge advances in transportation, and pave the way for flight times between Australia and the UK to be cut to 90 minutes.
Unlike other companies, such as Blue Origin and SpaceX, which plan to take tourists into space by rocket, Virgin Galactic's operation involves a horizontal launch, so is more suited to taking off from the first spaceports in Newquay and Sutherland.
Instead of a vertical launch, a carrier aircraft, dubbed "WhiteKnightTwo", carries "SpaceShipTwo" to 50,000ft before the plane releases it and it fires its rockets to blast through the Karman Line, which represents the boundary between Earth's atmosphere and outer space at 100km high. Six passengers will experience five minutes of weightlessness.
The craft then changes its wings into a shuttlecock shape, allowing it to glide back down to Earth.
"For Britain to be the first spaceport in Europe to be able to offer that service, because we have the legislation in place, because we've sorted out our infrastructure, that will be huge," said Major Peake.
"It's a very exciting time right now. Space tourism can come under some criticism as a sport for the rich, but ... that's how aviation started. What might be perceived as an expensive folly today actually can in future become a very efficient means of transportation.
"If you extend Virgin Galactic's principle of suborbital flight and improve the vehicles ... you could do London-to-Sydney in an hour and a half."
Andrew Kuh, the head of space flight policy at the UK Space Agency, who is speaking at London's Citadel festival next weekend, said: "The Space Industry Act 2018 has already put in place the legal framework and now we're working on the regulations to enable suborbital human space flight."We need to assess safety in a different environment."
More than 600 people have already paid $250,000 (£157,000) or put down deposits to fly aboard Virgin's suborbital flights, including the actors Leonardo DiCaprio and Kate Winslet. Stephen Hawking had also bought a ticket before his death last year.
Although Virgin Galactic's first flights are likely to launch from the US, Britain could be the first country for space tourism in Europe.Earlier this month the UK Space Agency announced the formation of a National Space Council and pledged £7.85 million funding to help Virgin Orbit establish a base at Spaceport Cornwall that would enable small satellite launch from in the early 2020s.
Chris Skidmore, the science minister, said: "The UK's geographic position provides a unique opportunity to place small satellites into orbit using vertically launched rockets.
We also want to enable horizontal launch from sites such as Spaceport Cornwall, from where aircraft and space planes could take payloads, and one day people, to space."
Britain is also working alongside the European Space Agency to build a "gateway" space station in the Moon's orbit, giving astronauts a stepping stone on the way back to the lunar surface, and eventually on to Mars.
