* Fed, BoE hold rates and push back against cuts

* Blistering stocks and bond rally now seen on hold

* Markets still price hefty easing by year-end

LONDON, Feb 1 (Reuters) - Traders eager for central banks to declare the start of interest rate cuts were dealt a further blow on Thursday as the Bank of England joined the U.S. Federal Reserve in dousing hopes of imminent monetary easing.

The BoE held rates at 16-year highs and said it needed more evidence that price pressures were falling sustainably before shifting course. Its policymakers were markedly split on the future rate path.

The Fed on Wednesday meanwhile shot down market bets for a March rate cut, sparking Wall Street's biggest daily rout since September.

Global stocks, which rose about 15% from October to January on hopes of a swift fall in borrowing costs, drooped on Thursday while bond markets stumbled and investors warned of a long wait for good news.

"We're in for a big range trade," said Jason Simpson, fixed income strategist at State Street's SPDR ETF unit.

"People may still buy on weakness in equities and bonds but it's going to be hard to really forge forward in terms of prices going up," he added, after last year's "over-excitable" rally.

TENSION

Markets price in a first quarter point Fed rate cut in May, having put the probability of a cut in March as high as 90% in recent weeks.

Traders on Thursday also turned more pessimistic on a BoE cut soon, with the chances of May cut at around 55% versus roughly 64% early in the day.

So the likes of the European Central Bank, Fed and BoE are now stuck between watching inflation fall and worrying it could rise again, investors and analysts said.

Data on Thursday showed euro zone inflation eased as expected last month but underlying price pressures fell less than forecast.

The BoE on Thursday chopped its inflation forecast for the coming months but warned it would rise back above its 2% target in the third quarter, and not return to target until late 2026, a year later than the BoE expected in November.

"There's this sort of tension between declining inflation and resilient labour markets and resilient growth," said Invesco senior fixed income manager Michael Siviter, discussing developed world trends broadly.

Rate cuts would come, he added, but central banks would face no pressure to ease swiftly unless economic growth deteriorated fast.

Sebastian Vismara, financial economist at BNY Mellon and a former BoE economist, said equities should be supported while economic growth holds up but government bonds would be volatile.

"Unless there is a more severe deterioration in the economy, central banks will be quite gradual and deliver less (easing) than what is priced in," he said.

Government bonds, which rallied along with stocks late last year, were "fairly valued for now", Invesco's Siviter said, adding that he would look to buy if yields rose.

U.S. 10-year Treasury yields, which fall as the price of the debt rises, are 110 basis points below October peaks, while German equivalents are down 85 bps .

Two-year UK gilt yields, trading at 4.23%, are comfortably below peaks around 5.5% hit last year.

Central banks had "ditched their tightening bias," Saxo Bank senior fixed income strategist Althea Spinozzi said, adding that "bonds can't rally much further as we don't know when rate cuts will start."

CATALYST?

With major central banks now watching economic data closely before making their next moves, markets are at the mercy of how inflation pans out.

"It's all going to be driven (by) inflation and jobs data, unless you have something hitting the wires and coming out there, which is unforeseen," said Ed Hutchings, head of rates at Aviva Investors, referring to events like a potential escalation in the Middle East or U.S. regional bank risks becoming systemic.

Over the longer term Hutchings favoured UK gilts over U.S. and eurozone bond markets , where more cuts are priced in, increasing the risk of sell-offs if the predictions prove incorrect.

Markets price roughly 145 bps worth of easing each by the Fed and ECB by year-end versus just over 100 bps by the BoE.

Financial conditions, which reflect broadly how easy it is for companies and households to borrow money, have loosened and become a focus for central bankers deciding when to pivot to rate cuts, investors said.

"Perhaps the BoE has learnt from the Fed in the autumn, where endorsing market pricing is seen as a dovish message, which then causes a rate rally, which then makes bringing inflation back to target even harder," said Mike Riddle, head of fixed income macro unconstrained at Allianz Global Investors.

(Reporting by Naomi Rovnick and Yoruk Bahceli; additional reporting by Dhara Ranasinghe; Editing by Dhara Ranasinghe and William Maclean)