* Yen edges up, global gloom counters BoJ rate cut
* Aussie retreats with other commodity currencies
* Drop in oil prices weakens risk appetite
* Sterling helped by pre-referendum EU draft deal
By Patrick Graham
LONDON, Feb 2 (Reuters) - The yen inched higher on Tuesday as another drop in oil and stock markets sent investors back to traditional safe havens, hammering commodity-dependent currencies in the process.
The Australian and New Zealand dollars both sank almost 1 percent in midday trade in Europe, while the Canadian dollar and Norwegian crown - both heavily dependent on oil revenues for capital inflows - fell by more than half a percent.
The almost 4-percent fall in crude prices swept away the more positive tone to markets created by a shock interest rate cut into negative territory by the Bank of Japan last week.
"The gloom is definitely back," said a dealer with an international bank in London.
The yen gained 0.3 percent against the dollar to 120.63 yen JPY= , though in the wake of the BoJ decision it is still almost 5 yen weaker than a peak of 115.97 hit two weeks ago.
Constantin Bolz, director for FX strategy with UBS Wealth Management in Zurich, said the move to curb more yen gains would continue to reverberate through markets in coming weeks.
"If they had waited any longer I think the market would have gone ahead and pushed dollar-yen even lower," he said, citing estimates that Japanese companies had planned this year with the yen around 115-118 and would have been hurt beyond those levels.
"Secondly, the fact that they have gone towards negative rates opens them a completely new opportunity set. They have always said they would not do negative rates and now that they have, if need be they can go further."
Market participants said the dollar was likely to find support at levels near 120 yen in the near term, the prospect of negative rates from the middle of February making it more costly for speculators to hold on to long positions in the yen.
"I think there is no doubt that it has become harder to try for the downside in the dollar against the yen," said one trader with a Japanese bank in Singapore.
The euro, which has also benefited from safe haven flows in the past month, rose 0.3 percent to $1.0920 EUR= , within the $1.0711-$1.0985 range it has held since the start of the year.
Along with U.S. jobs data on Friday, the Bank of England's quarterly inflation report is this week's main set piece.
Sterling, a big riser on the back of bullish economic data on Monday, tested overnight highs against the dollar after the publication of proposals for a deal on changing the terms of Britain's EU membership ahead of a referendum on the issue. GBP=D4
The pound, down around 6 percent in the past two months on concerns that the campaign to withdraw from the EU has some traction, traded flat on the day at $1.4435 and 0.2 percent weaker against the euro at 75.70 pence after the publication. EURGBP=
(Editing by Louise Ireland and John Stonestreet)