Gordon Brown said today he intends to "keep going" as Labour leader even if the party loses the general election.

The prime minister signalled his intention to carry on in the event of a drubbing at the polls as part of a wide-ranging interview with BBC Radio 4's Woman's Hour programme this morning, in which he also admitted that allegations that he sometimes bullied his staff had been "damaging".

The prime minister was put on the spot over his plans amid growing speculation that voters could return a minority government after the general election, which is expected to take place on 6 May.

Two polls at the weekend provided further evidence that the Tory lead is shrinking. YouGov in the Sunday Times gave the Tories (on 37%) a four-point lead over Labour, down one point on the Conservative lead in the Sunday Times poll the week before.

ICM in the Sunday Telegraph gave the Tories (on 38%) a seven-point lead over Labour, down two points from the Conservative lead in the ICM poll for the same paper seven days earlier.

Brown insisted he would "keep going" in response to being asked whether he owed it to Labour to quit as leader if he failed to secure a decent majority.

He told the programme: "I owe it to people to continue and complete the work that we've started of taking this country out of the global, financial recession. To be honest, going around the country, I feel there's more to do to improve the health service, more to do to give people better opportunities, more to do for women on maternity pay and equal pay, more to do against the discriminations that still exist. We've got this campaign to get more women in the boardroom as well."

Pressed on whether he would quit, he said: "No, I'll keep going because I want a majority. I'll keep going."

His comments followed a report in today's Times which quoted an unnamed senior minister suggesting that Brown would hope to remain Labour leader in the event of defeat at the polls.

The minister was quoted as saying: "Don't underestimate Gordon. Unless the rejection at the polls is large and personal, there is no reason for him to go quickly."

Brown was pressed on the programme about the extent of detail voters could expect on public spending before the general election.

He said there would be "more information" in the budget, but admitted there was "uncertainty" because of unemployment.

"We have announced cuts and there will be more information in the budget," he said.

He added: "At the moment we are not absolutely sure what's happening to employment and unemployment. We don't know yet what savings we can get from cutting or keeping unemployment down, but that runs into billions of pounds. If we have these savings, we can use them to fund departments. If we don't have these savings, it makes it more difficult. So there is a degree of uncertainty at the moment about what we can do in the future."

He insisted that hospitals, schools and policing would have their funding protected. He acknowledged that was only for two years, but sought to reassure voters that the protection would remain after that period.

"I think you can be reasonably sure that the protection for health and education and policing will be continued," he said. "You will get the spending round in due course."

Brown also told the programme that his decision to begin talking publicly about his personal life, which included a recent TV interview with Piers Morgan in which he talked about the death of his baby daughter, Jennifer Jane, was because the way he was represented in the press "is just not me".

He had decided to open himself up to any questions to show "that there is no way I can be as one-dimensional as the newspapers are presenting so I decided that was the best thing to do".

The Morgan interview was watched by 4.2 million people, twice the number who watched David Cameron feature in a fly-on-the-wall documentary on the same channel and Sunday evening slot last night.

The prime minister admitted that allegations in a book by the Observer's Andrew Rawnsley that he had bullied staff had been "damaging" but defended his behaviour in the job and indicated he had not modified his conduct since.

"I'm a very tough person," he said. "I don't think you can be in a job I am coming from a pretty ordinary background ... without being strong-willed and determined."

He also rejected claims that he treated female colleagues as "little more than window dressing" – an accusation levelled at him by Caroline Flint when she stepped down as Europe minister last summer – or that he felt more comfortable with men than women. "No, I feel more comfortable with women," he laughed, "and I have worked very closely with the women who have worked with me."