Rail journeys from London to Scotland could be cut to under three hours, Transport Secretary Patrick McLoughlin has said.
The £34 billion High Speed 2 scheme to northern England could be extended over the border, slashing times by about an hour.
But the project is mired in controversy for the Tory party, with parts of the line cutting through swathes of countryside in Conservative heartlands.
Mr McLoughlin promised compensation for people affected but insisted the massive scheme should go ahead.
"I hear those voices who say High Speed 2 is too costly, who say we can muddle through, and yes, the easy option would be to do nothing. It always is. But my answer is that we can't afford not to build it; our competitors around the world are investing in the best transport, and we must too," he said.
In his speech to the Conservative party conference in Birmingham, he claimed that "no big infrastructure project is ever done without great controversy", adding: "Once they are built, people rely on them."
Officials would investigate extending the high speed line, initially planned from London to Birmingham with later stages to Leeds and Manchester, north of the border, he said.
"I want even more parts of our country to benefit. We're launching a study on the way to get fast journeys further north still, with the aim of getting the journey from Scotland to London to under three hours and making sure the north-east benefits too, because this will be a scheme for every person in Britain."
Earlier this year the Government unveiled a commission to prepare ideas for expanding airport capacity around London.
The Tories, previously opposed to a third runway at Heathrow, claim that more space is needed to boost British business, and London Mayor Boris Johnson favours an ambitious scheme for a new airport on an island in the Thames estuary.
The Transport Secretary said: "The runways are filling up and the jets are circling in our skies.
"That's hitting our prosperity. It's bad for the environment, it's putting off investors, it's costing jobs and it's holding Britain back.
"We need to make sure we have airports that are globally competitive, where you can connect to places all over the world.
"Of course there are all sorts of ideas: Boris wants an island, I want an answer."