(Updates at 1144 GMT after BoE decision)

By Harry Robertson, Sruthi Shankar and Ankur Banerjee

LONDON/SINGAPORE, Aug 1 (Reuters) - The dollar rallied

on Thursday after falling the previous day as central banks

continued to roil currency markets, while sterling fell to a

four-week low after the Bank of England (BoE) cut interest rates

from a 16-year high.

The dollar index, which tracks the currency against

six others, was up 0.35% at 104.40. It fell 0.4% on Wednesday

after the Federal Reserve held rates steady but opened the door

to reducing borrowing costs in September.

Chris Turner, head of global markets at ING, said

geopolitical tensions and a slowing global economy were likely

supporting the dollar, a traditional "safe haven" for investors

at moments of stress, even with the Fed heading for rate cuts.

"The geopolitical and the macro environment elsewhere in the

world isn't actually great," he said. "Obviously we've still got

some real tensions in the Middle East, and the manufacturing

sector is seemingly in recession across large parts of Europe

and in Asia."

Hamas leader Ismail Haniyeh was assassinated in Tehran on

Wednesday, an attack that drew threats of revenge against Israel

and fuelled fears of a wider Middle East war.

The pound fell to $1.2752 after the BoE cut rates,

its lowest since early July. It was last down 0.51% at $1.279,

slightly above where it stood before the decision, ahead of

which markets saw a roughly 60% chance of a cut.

BoE Governor Andrew Bailey - who led the 5-4 decision to

lower rates by a quarter-point to 5% - said the BoE's Monetary

Policy Committee would move cautiously going forward.

"If you look at the headlines that Bailey produced: caution

on cutting too quickly or by too much, it implies to me that

they're looking at a sort of a steady quarterly pace of

reductions," said Colin Asher, economist at Mizuho.

"The start of lower interest rates is underway, but

reasonably gradually."

Sterling has fallen from a one-year high above $1.30 in

mid-July as investors' views on BoE rate cuts have shifted.

The euro touched a three-week low of $1.0777 and

was last down 0.36%.

BOJ BUCKS EASING TREND

Japan's yen slipped, with the dollar up 0.4% at

150.525 yen.

The yen jumped around 1.8% the previous day after the BOJ

raised rates for a second time this year. It rallied 7.3% in

July, its strongest monthly performance since November 2022,

after starting the month rooted near 38-year lows.

Intervention by Japanese authorities to boost the currency

kicked off the move higher, combining with a narrowing of the

U.S.-Japan interest rate gap to trigger an unwind of profitable

carry trades, in which traders borrow the yen at low rates to

invest in dollar-priced assets for higher returns.

Fed Chair Jerome Powell on Wednesday stressed that the

central bank was also focused on keeping the labour market

healthy, adding new emphasis to Friday's U.S. jobs report for

July.

It is expected to show that employers added 175,000 jobs

during the month, a step down from 206,000 in June. Data on

weekly jobless claims is due later on Thursday.

Traders are now anticipating 72 bps of easing this year

. The Fed meeting "has bolstered market expectations

that bigger rate cuts remain likely, and will be heavily

influenced by how the economy progresses from here", said Charu

Chanana, head of currency strategy at Saxo.