Speaking in Parliament on Tuesday, Mr. Johnson acknowledged that the project had been troubled by poor management and promised to appoint a minister to oversee it. “We have to have the guts and foresight to drive it through,” he added, noting that most big infrastructure plans provoke opposition.

Mr. Johnson also announced on Tuesday support for smaller-scale travel projects in northern England, including additional funds for buses and an upgrade to a rail link between the cities of Manchester and Leeds. Critics of High Speed 2 have frequently declared that its budget should instead be spent on ideas like those.

There are many such critics in Mr. Johnson’s camp. Some are lawmakers concerned about disruption and damage to countryside in their districts — the first phase of the route rips without stopping through traditional Conservative heartlands in southern England. Others — including the prime minister’s most prominent aide, Dominic Cummings — consider it unacceptable value for money.

Once expected to cost around 33 billion pounds — roughly $40 billion — the plan is now estimated at £106 billion. The schedule has slipped, too: The Birmingham phase was originally supposed to be finished by 2026, with cities further north connected by 2033.

The opposition Labour Party attacked the government’s record. “HS2 has been appallingly mismanaged by the Conservative Party, which has failed to deliver a single major infrastructure project on time or within budget,” said Andy McDonald, who speaks for Labour on transport issues.

Supporters say the project’s difficulties reflect the scale of its ambition. Trains would travel at speeds up to 224 miles per hour, faster than any other train service in Europe, and the railroad would accommodate as many as 18 services per hour.

They argue that the new railroad is necessary to ease congestion on the core of Britain’s rail network, allowing for more local services on lines currently shared with long-distance expresses.