Following Mr Brown's election as leader yesterday, Mr Cameron's said: "I am looking forward to the challenge."
Mr Brown's election coincided with a poll putting Labour ahead of the Tories for the first time since October. The Daily Mail claimed today that Mr Brown is planning to exploit Labour's bounce in the polls by calling a general election as early as next spring.
Mr Cameron was upbeat about the Conservatives' prospects as he promised to pursue a "relentlessly positive agenda".
But speaking on BBC Radio 4's Today programme, he immediately hit out at the prime minister-in-waiting, saying he could not "provide the change Britain needs" after a decade at Tony Blair's side.
Mr Cameron claimed that the Conservatives now occupied the centre ground and promised they offered "exciting and inspiring alternative" to the government.
He also dismissed the Tories' dip in the polls. "The only time that the state of opinion in this country on the parties has been tested this year was the local elections, where my party won 40% of the vote, 900 council seats, made gains all across the country," he said.
The "very big changes" he has made to the Conservative approach, over tax, health and education, proved it had adapted to new challenges, Mr Cameron claimed.
"The party has changed - it is in the middle ground; it is challenging for power; it is much more relevant to people's concerns today in terms of really fighting the fight on health and education and crime."
Mr Cameron said he would be happy to work alongside Mr Brown when he "does the right thing".
But he added: "My issue with Gordon Brown is that I don't believe he can provide the change that Britain needs."
