Rachel Reeves has said she had had “a tough day” and had been “clearly upset”, as she gave her first interview since crying in the House of Commons on Wednesday.

She did not go into details behind the incident saying she had been dealing with “a personal issue” adding: “Today’s a new day and I’m just cracking on with the job.”

The chancellor was speaking after making a surprise appearance alongside Sir Keir Starmer to unveil the government’s 10-year plan for the NHS.

Government borrowing costs initially rose following Reeves’ tearful appearance at Prime Minister’s Questions, when Sir Keir initially failed to guarantee that the chancellor would keep her job.

The fall was partially reversed after Sir Keir insisted he was “in lockstep” with his chancellor, who he said would be in her job “for a very long time to come”.

In a bid to put on a united front, the chancellor unexpectedly joined Sir Keir and Health Secretary Wes Streeting at a hospital in East London to set out details of new neighbourhood health centres.

As she addressed staff, Reeves was smiling broadly and later shared a hug with the prime minister.

Speaking to broadcasters after the event, Reeves said “My job as chancellor at 12 o’clock on a Wednesday is to be at PMQs next to the prime minister, supporting the government and that’s what I tried to do.”

She added: “I think all your viewers have had tough days, for personal reasons, for whatever reasons. I happened to be on the camera when I had a tough day.”

She said she was “totally” up for the job of chancellor and asked if she was surprised the prime minister had not unequivocally backed her in Parliament replied: “People can see that Keir and me are a team.”

“We fought the election together, we changed the Labour Party together so that we could be in the position to return to power and over the past year we’ve worked in lockstep together.”

Sir Keir praised his chancellor, telling the audience: “I think it’s just fantastic that she is here.”

He said decisions made by Reeves had allowed the government to “invest record amounts in the NHS”.

Asked if he had been aware that his chancellor had been crying next to him in the House of Commons, Sir Keir said he “hadn’t appreciated what was happening” as he was “literally up and down” answering questions.

“No prime minister ever has had side conversations in PMQs. It does happen in other debates when there is a bit more time, but in PMQs it is bang, bang, bang, bang.”

He said the incident was due to “a personal issue and I am certainly not going to say anything more about that”.

Speaking to Virgin Radio earlier in the day, the prime minister said all people could be caught “off guard” and that he had a long chat with Reeves after the incident.

“She’s very resilient and strong is Rachel,” he added.

Speculation about Reeves’ future had been growing after Labour rebels forced the government to give up some of its benefits changes and in so doing put a £5bn hole in the chancellor’s spending plans.

In order to meet her self-imposed borrowing rules, she is now likely to have to consider cutting public spending or raising taxes at the Budget in autumn.

Asked if taxes would be going up, Reeves said she wouldn’t “speculate” but added: “Of course there is a cost to the welfare changes that Parliament voted through this week and that will be reflected in the Budget.”

In a sign that she would not be changing her own restrictions on borrowing, the chancellor said “stability that we’ve been able to return to the economy… is only possible because of the fiscal discipline which is underpinned by the fiscal rules”.

Reeves’s two main rules are not to borrow to fund day-to-day public spending; and to get debt falling as a share of the UK economic output by 2029/30.

In her speech, she also said the boost to NHS spending would not “have been possible” without the measures she took in last year’s Budget.

Speaking to BBC Breakfast on Thursday, shadow chancellor Mel Stride said he “felt for” Reeves, and the incident showed politicians “are all human beings”.

But he accused the government of making “serious mistakes” and “bungling and chaos”, which he predicted would lead to tax rises in the autumn.

Rachael Maskell, one of the Labour MPs who led efforts to block the government’s benefits bill, told the BBC on Wednesday that when trying to find money, the government should “look at those with the broadest shoulders”.

“We do need to look at things like a wealth tax or equalisation of capital gains tax,” she said.

On Thursday, the government announced that its Universal Credit and Personal Independence Bill would be renamed the Universal Credit Bill, after the legislation was gutted of significant measures relating to the personal independence payment.

The cost of government borrowing surged after Reeves’ emotional appearance in the Commons, but fell back after she received backing from the prime minister.

One analyst told the BBC the initial rise reflected concern in the financial markets that if she left her job then control over the government’s finances would weaken.

Will Walker Arnott, head of private clients at the bank Charles Stanley, told the BBC’s Today programme: “It looks to me like this is a rare example of financial markets actually enhancing the career prospects of a politician.”