In a speech to Labour's conference, he said the Tories could not be trusted to run the economy and vowed Labour would not stop fighting for a "fair society".
He also pledged to scrap prescription charges for people in England with cancer from next year.
And in a surprise move, Mr Brown was introduced to delegates by wife Sarah.
In a more personal conference address than normal, Mr Brown said he had been "stung" by criticism of his decision to scrap the 10p tax rate and vowed he would never again be accused of not being on the side of "hard working families".
He also took a swipe at politicians who use their families to gain media coverage, saying: "My children aren't props - they're people."
The prime minister was under pressure to reassert his authority over the party and bury talk of a leadership challenge.
He told Labour rebels it was their "duty" to focus on the challenges facing the country rather than internal party rows.
The theme running through the speech was fairness and he pledged to create "a Britain of fair chances for all and fair rules applied to all".
He repeated his plan to extend free nursery places for all two-year-olds over the next 10 years - and he pledged to enshrine in law Labour's promise to end child poverty.
He highlighted a £300m plan to offer free computers and internet access for more than a million children from low income families to boost their chances in the jobs market.
And he said that in addition to free prescriptions for people with cancer, charges would also be waived for anyone suffering from a long-term illness.
Mr Brown also hailed Labour's latest crackdowns on benefit cheats and crime.
"The dole is only for those looking for work or actively preparing for it. That's only fair to the people pulling their weight. "And let me be clear about the new Labour policy on crime; taking action on the causes of crime will never mean indulging those who perpetrate it. Fairness demands that we both punish and prevent."
No time for a novice, Brown says
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