Speaking at his last quarterly inflation report press conference, King said discussions among Europe's central bank chiefs revealed a huge amount of opposition to a transaction tax despite public backing from politicians. A long-time critic of the so-called Tobin tax, he said a charge on individual financial transactions, which several EU countries have supported in principle, was still year's away.
"Even politicians who are publicly in favour have misgivings," he said.
His intervention is bound to upset anti-poverty campaigners who have succeeded in persuading 11 eurozone countries to introduce the tax on stock, bond and derivatives transactions next January, raising up to €35bn (£29bn) a year.
King said the tax remained several years from implementation as there remained little agreement on which transactions to tax.
The governor said the outlook for the UK economy had improved with growth likely to reach 0.5% in the second quarter of 2013, in addition to the 0.3% registered in the first three months of the year, giving an overall 1% rise of this year.
The central bank gave no sign it was on the verge adding further stimulus, describing policy as "highly stimulatory".
"The economy is likely to see a modest and sustained recovery over the next three years," the central bank said, though it added that the recovery would "remain weak by historical standards".
This represents the cheeriest outlook for a couple of years during which it has steadily downgraded its growth forecasts.
It said the recovery was likely to be "slow but sustained".
Britain has been suffering its slowest economic recovery in decades, and the Bank forecast that GDP was more likely than not to remain below its pre-crisis level for another year or so.
"The main risks to the recovery continue to emanate from abroad," the BoE said.
Figures earlier on Wednesday showed that France's economy shrank in the first three months of 2013, and weak demand in the eurozone as a whole has been a major headwind for Britain's exporters in recent years.
The central bank forecast that inflation in two years' time was likely to be around its 2% target – down from the 2.3% it forecast in February – and that inflation would average below 2% for the rest of the forecast period.
Inflation has exceeded the central bank's 2% target since December 2009, which is one reason why the BoE has not increased bond purchases under the quantitative easing programme (QE) past the £375bn reached in October.
The Bank generally sets monetary policy with the aim of ensuring that inflation has returned to its 2% target within two to three years, and the chancellor, George Osborne, has recently encouraged the bank to take a flexible approach.
Incoming bank governor Mark Carney – who takes over from King in July – is also a fan of long-term interest rate guidance to stimulate the economy.
Howard Archer, chief economist at analysts IHS Global Insight, said it was likely the Bank will expand QE in the coming months.
"It is notable that in his opening remarks, King said 'this is no time to be complacent – we must press on to ensure a recovery and bring down unemployment'.
"We suspect that Carney will be keen to try and build up escape velocity from the economy's extended softness and will be keen to quickly establish his presence after arriving at the start of July.
"Of course, Carney will only have one vote out of nine in the MPC as does King, but we suspect that he will be able to carry a majority of MPC members with him should he favour more help for the economy."
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