Boris Johnson’s government might be forced to delay its first budget after the former chancellor Sajid Javid walked out last week in a row about his special advisers.

The transport secretary, Grant Shapps, said Javid’s replacement, Rishi Sunak, may have to choose a new date beyond the timetabled budget due on 11 March.

Asked on the BBC’s Andrew Marr Show on Sunday if the budget would be delayed, Shapps said: “The guy’s only been in place a few days, let’s give him a few days to decide on the date.”

The budget had originally been scheduled for November but had to be pushed back because of the general election.

Javid dramatically quit his role after he was told his political advisers would be sacked and instead parts of No 11 would be merged with Downing Street.

The Conservative party has not committed itself to any specific tax rises or significant infrastructure investment. There had been suggestions the government was toying with an effective mansion tax on the country’s most expensive homes to raise revenue but that idea has reportedly been discarded after concerns from backbench Tory MPs.

Shapps said in his Marr interview: “I can tell you that we are absolutely kind of determined to deliver a big uplift in the infrastructure in this country.

“We’ve just been talking about HS2. The interesting thing about HS2, for example, is that it only takes per year about 4% of the capital budget that we have allocated each year. So there is a lot more that you’ll still be expecting us to do – powerhouse rail and all these other things. The buses, the bike – the cycle lanes.”

Reports that the China Railway Construction Corporation had been in contact with HS2 Ltd about building the line were confirmed by Shapps, but he said the government itself was not in active talks over the project.

China’s state railway company has suggested it could build the line in five years and more cheaply than current budget estimates, which have spiralled to more than £100bn.

Asked by Marr if the government was talking to China about taking over HS2, Shapps said: “No. No. That’s not the case, no. They have clearly had a letter sent to HS2 Ltd. There’s been no conversation with me as minister, as the secretary of state.”

Shapps said a five-year timescale to build the project seemed unlikely considering the standards of British construction.

“The Chinese build these things fast but they don’t have our planning system, our legal system. They don’t have to respect people’s property rights in the same way,” he said.

Earlier, Shapps played down reports that Downing Street wanted to axe the TV licence fee and fund the BBC through viewer subscriptions.

No 10 had signalled a fresh onslaught on the broadcaster, with the Sunday Times quoting a senior source as saying the BBC could be forced to sell off most of its radio stations in a “massive pruning back” of its activities.

The source told the paper Boris Johnson was “really strident” on the need for serious reform, and they said there would be a consultation on replacing the licence fee with a subscription model, adding: “We will whack it.”

Shapps said that while there was a consultation under way into decriminalising non-payment of the licence fee, there were no “preordained” decisions on future funding models.