Sir Keir Starmer has signalled he will invest billions in transport, schools and hospitals as he insisted he would not be “knocked off course” by the turbulence of his first 100 days in office.

The Prime Minister said he would not get “bogged down” by rows over his former chief of staff Sue Gray or the controversy over his acceptance of gifts from donors.

And he told The Guardian he wanted to be able to show voters “a bit of the sunny uplands” after the Labour administration has spent months painting a gloomy picture of the economic inheritance they received.

In a sign that Chancellor Rachel Reeves’ Budget will include significant public investment, he said: “While other countries have powered ahead, building big and taking advantage of new technology, Britain has been left to make do with their out-of-date ideas and out-of-date service.”

The Prime Minister said it was “common sense to invest and build”.

“If working people can’t afford a decent home, they can’t build good lives and careers,” he said.

“When people can’t get to work because public transport is poor, productivity suffers. If schools are crumbling over our children’s heads, how can we expect them to learn the skills they need?

“And NHS waiting lists are through the roof because there has been nowhere near enough investment in hospitals and the technology that could make treatment more efficient and more effective.”

Saturday marks the 100th day of Sir Keir’s premiership and he acknowledged it had not gone smoothly.

“You’re going to get side winds all the time. If you’re not going to get knocked off course, you’ve got to know where we’re headed,” he said.

“The moment I allow myself to get too bogged down in the side winds is the point that other governments have gone wrong, in my view, because they’ve lost sight of what the real point of government is.”

But he added: “It’s been very much what I expected. It’s proved the thesis that government is tougher, but that government is better.

“Tougher because you’ve got to take tough decisions. Better, because you can take decisions and make a difference.”

He admitted the focus on the gifts of clothing, glasses, football and concert tickets he had received had been difficult, particularly as his family got dragged into the row. His wife Victoria received clothing while the Prime Minister said the use of an apartment provided by Labour peer Lord Alli was to allow his son space to study for his GCSEs.

“I’m not going to pretend its pleasant, because of course it’s not pleasant, but it wasn’t a first-time experience, and I doubt it will be a last one either,” he told The Guardian.

But he said the furore around donations was “a million miles away” from the Covid-era partygate and PPE scandals which hit the Tories.

The October 30 Budget will be the next big opportunity for Sir Keir’s government to demonstrate what it stands for but the Chancellor has already warned that tough decisions will be needed to repair the public finances.

Sir Keir has insisted the short-term struggles would be worth it in the end.

“I needed to get to ‘what’s it for?’,” he said. “Being able to say to people that this is what it begins to look like, this is your better life at the end of it … We cannot deliver what we need to deliver until we fix the foundations.”