By Samuel Indyk

LONDON(Reuters) - The pound fell against a rebounding dollar on Tuesday even as U.S. President Donald Trump stopped short of implementing tariffs as signs of a softening British labour market reinforced expectations for a February rate cut from the Bank of England.

Trump did not immediately impose tariffs on U.S. imports on his first day back in the White House but told reporters he was considering import tariffs of around 25% on Canada and Mexico by Feb. 1, challenging suggestions his trade policy may be more gradual.

The dollar fell sharply on Monday after Trump's first day included no specific news on tariffs, lifting sterling and other trade-exposed currencies.

The pound was down 0.6% against the dollar on Tuesday at $1.2255, having jumped 1.3% on Monday, its biggest daily jump since November 2023.

"Expect a lot of headline-related noise this week, with action in the crosses based on tariff threat perception," said Francesco Pesole, FX strategist at ING.

Meanwhile, British pay growth stayed stubbornly strong in the three months to November, although other measures on the health of the labour market indicated a softening employment picture.

Data provided by employers to the tax authorities showed the number of employees dropped by 47,000 in December, the sharpest fall since November 2020, following a 32,000 drop a month earlier.

Market expectations for a BoE rate cut in February held firm after the data, with traders pricing in around an 85% chance of a quarter-point cut.

"This data will give the Bank of England a green light to cut in February," said Dominic Bunning, head of G10 FX strategy at Nomura.

"There wasn't really a huge shock in the data so there's no reason to think differently having seen the numbers."

The pound was little changed against the euro at 84.5 pence.

ING's Pesole believes there may be upside risks for euro-sterling in the near term as "markets can still price in more Bank of England easing and continue to embed idiosyncratic GBP risks related to higher borrowing rates."

The 10-year gilt yield was down 0.5 basis points on Tuesday, falling for a fifth straight day, after touching its highest level since 2008 on Jan. 9.

(Reporting by Samuel Indyk; Editing by Christina Fincher)