George Osborne will use Wednesday’s budget to set in motion plans for a high-speed railway line from Manchester to Leeds and an 18-mile underground road tunnel beneath the Peak District.

The chancellor will also promise to “prioritise” a north-south link through central London as he accepts the final recommendations of the National Infrastructure Commission, led by former Labour peer Lord Adonis, which are being published on Tuesday.

The Treasury said Osborne would bring forward capital spending in order to invest in the HS3 high-speed rail line, the trans-Pennine tunnel and Crossrail 2, with initial funding amounting to £300m.

Adonis said: “If the north is to become a powerhouse, it has to be better connected. Leeds and Manchester are just 40 miles apart but there is no quick and easy way to travel between the two. In rush hour, it can take more than two hours by car; by train, it can be almost an hour.”

Adonis said the aim should be journey times of just half an hour and it was not acceptable to wait decades for the improvements. The Labour peer set a target that the travel time between the two cities should be 40 minutes by 2022.

“A better connected north will be better for jobs, better for families and better for Britain,” he said. “The work should begin as quickly as possible.”

The move is likely to be welcomed by MPs in northern England and unlikely to cause the sort of controversy aroused by the HS2 London to Manchester link, which has been fiercely resisted by local communities, seen costs spiral to £50bn and triggered warnings about the risks of derailment.

Jonny Reynolds, the MP for Stalybridge and Hyde, which is on the HS3 route, said the aim was a transport system that would allow people to easily live in one northern city and work in another.

Work on the next stage of designs for another high speed rail network that would include linking Sheffield and Liverpool is also to feature in the new plans.

Questions may be raised about whether a cash injection of £300m will come close to ensuring the projects are actually delivered; the total cost of these projects usually stretches to billions of pounds.

The Treasury appeared to suggest that most of the money to be announced on Wednesday would go towards the early planning stages of the projects, but some sources insisted it would be used to kickstart the work.

Osborne insisted that the tough economic situation would not stop him making “bold decisions and big investments” to help Britain lead the world in infrastructure. The plans will also see the launch of a £1.2bn fund to release brownfield land to build more than 30,000 starter homes across the country.

The Adonis report calls for “immediate and very significant investment for action now” to cut journey times. He also wants urgent improvements to the M62, which runs between Liverpool and Hull.

The trans-Pennine tunnel would be Europe’s longest road tunnel, although experts have warned that the psychological difficulties facing drivers travelling so far underground would have to be considered before it got the go ahead.

The link could dramatically cut the time it takes to travel from Sheffield to Manchester and help drivers avoid the poor weather conditions sometimes experienced on the A628 Woodhead Pass. But the predicted price tag is £6bn, with the £75m promised this week only covering plans to explore various options.

Osborne’s budget willalso deliver on Conservative manifesto promises to raise the personal allowance and the income rate at which the 40p higher tax rate takes effect. But he warned at the weekend that he need to impose further cuts to government spending of £4bn by 2020. One plan is for a stealth tax that will result in motorists and homeowners paying more in insurance.

The chancellor has also “pencilled in” an increase in fuel duty of 1.3%, or 0.75p, but he is under pressure from his own backbenchers to opt for a freeze instead. That would cost him almost £350m.

Osborne has been approached by a number of Tory MPs about the issue. Karl McCartney, the Conservative MP for Lincoln, warned that drivers already paid “some of the highest direct and indirect taxes in the world” and welcomed the fact that the Tories had frozen the duty so far.

Philip Davies, another Conservative MP, opposes any increase, although he said he would view the budget “in the whole”. “If 50 measures are great and one is disappointing, then that is not bad,” he said, arguing that he wanted to see spending cuts rather than tax rises.

Meanwhile, campaigners and the Labour party are calling on the government to rethink a move under which the Treasury no longer produces data on how different socioeconomic groups are hit in cash terms by budget measures. The “distributional analysis” allowed people to quickly see how the poorest fared.

A letter to the Guardian signed by a number of charities including the Equality Trust warns that the change “is a serious mistake”.

A Treasury spokesman insisted that a distributional analysis was still published but simply looked at the “share of spending received” rather than the change in cash terms.