LONDON - Gordon Brown vowed to fight on as Britain's prime minister on Sunday after a poll showed support for his Labour party had firmed slightly over the past month despite a failed leadership coup last week.

The survey by ICM in the Sunday Telegraph found support for Labour was one point higher than a month ago at 30 percent. The Conservatives were steady at 40 percent and the Liberal Democrats down one point at 18 percent.

The poll, conducted on January 6-7, showed more voters thought Labour would do better without Brown as leader than worse, but the margin, 41 percent versus 35 percent, was relatively small.

By contrast a YouGov poll in the Sun on Friday suggested 67 percent of voters either had no confidence in the Labour party or less confidence after Wednesday's unsuccessful putsch.

Two former cabinet ministers called for a secret ballot of Labour parliamentarians to decide if Brown should lead the party into an election due within the next five months.

The call failed to win any high-level support but the length of time it took some colleagues to come to Brown's aid raised renewed questions about his authority.

In an interview with The News Of The World, Brown played down Wednesday's incident and said he was focussed on the big choices that would shape Britain over the next decade.

I'm sorry it happened. I think it was a form of silliness, he said. I am the prime minister and am determined to remain so. I am determined, I am resolute.

Sunday's ICM poll, if repeated at an election, would give the Conservatives a parliamentary majority of just 16 seats.

Markets are concerned the election could produce a hung parliament or a government so weak it would not be able to take the tough measures needed to cut Britain's budget deficit.

Conservative leader David Cameron said his party would cut the deficit -- running at a record 12.6 percent of GDP -- faster and further than Labour, but refused to put figures on the likely extent of spending cuts.

We think we have to go further than what the government say, and we have to start earlier, Cameron told the BBC's Andrew Marr programme.

The government plans to halve the deficit over four years but is reluctant to cut back spending until economic recovery is assured.

While Brown has stressed the need to support growth, chancellor Alistair Darling has talked openly about the need for spending cuts and the possibility the deficit could be cut more quickly if the recovery is strong enough.

Once recovery is established we have to act, Darling told the Times in an interview published on Saturday. The next spending review will be the toughest we have had for 20 years.

Darling's strong words raised speculation that a weakened Brown had been forced to accept his tougher line on budget cuts.

(Editing by Janet Lawrence)