LONDON (Reuters) - Prime Minister Gordon Brown's popularity is at its lowest since he came to power in June, a poll showed on Sunday, amid reports of clashes with his ministers and criticism of the bailout of Northern Rock bank.

In a YouGov poll of nearly 2,000 people published in the Sunday Times, 33 percent thought Brown was doing a good job as prime minister, against 43 percent who said they thought he was doing badly.

Last month 59 percent though he was doing well, compared to 29 percent who said he was doing a bad job.

The Conservative party is now six points ahead of Labour, up three from last month, the poll showed. The Conservatives are unchanged on 41 percent, while Labour has slipped to 35 percent. The Liberal Democrats are up two at 13 percent.

Brown, who took over as prime minister from Tony Blair in June, enjoyed a brief honeymoon period at first as his government weathered an attempted bombing, floods in southern England and outbreaks of foot-and-mouth disease.

But he was widely pilloried for not calling an autumn general election despite letting it be known he was considering it.

Opposition leader David Cameron -- who many observers say has performed well against Brown during his weekly questioning of the prime minister in parliament -- also accuses him of stealing Conservative policy ideas.

The media are now reporting that an increasingly stressed Brown is rounding on his own team.

Last week security minister Lord West backtracked from comments about government plans on holding terrorist suspects without charge after a meeting with the prime minister, and Foreign Secretary David Miliband was reported to have altered a speech about Europe after intervention from Brown.

In addition, the former finance minister's government is now coming under pressure to nationalise ailing mortgage bank Northern Rock, which owes the Bank of England over 20 billion pounds.

The Treasury and the Bank of England provided emergency funding and guaranteed depositors' funds when the bank was hit by a global credit crunch during the summer.

But opposition politicians are angry about discussions to sell Northern Rock given that it could mean providing a private buyer with government support.

The latest poll comes as the BBC kicks off a three-part series of interviews with Blair, in the first of which he says there were "disagreements or tensions" with Gordon Brown when the latter was finance minister to Blair's prime minister.