* FTSE, sterling calm as UK heads to polls

* Topix hits record top, S&P 500 futures steady

* Odds narrow on Sept Fed cut after soft dataGraphic: World FX rates http://tmsnrt.rs/2egbfVh

LONDON/SYDNEY, July 4 (Reuters) - World stocks clocked up more record highs on Thursday after U.S. data had narrowed the odds on a September Fed interest rate cut, while Europe was on politics watch again as UK voters headed to the polls in national elections.

The July 4 holiday in the United States made for thin trading, amplified as investors tried to sit on their hands to see just how large a majority the Labour Party might get when UK vote results begin to come out late in the evening.

Markets are well prepared for a change given opinion polls have for months put the centre-left party on course for a landslide victory over the Conservatives who have held power for 14 years, including both for Brexit and the COVID-19 pandemic.

"Having been very negative of sterling for a very long time, institutional investors are actually going into this election quite neutral," said Michael Metcalfe, head of macro strategy at State Street Global Markets.

That is partly because political risk has surged in the likes of France which holds the second round of its parliamentary elections in three days' time, and in the United States ahead of its Presidential vote in November.

"The UK, oddly, has ended up with a neutral position in the middle," Metcalfe said. "Also, I don't think at any point has the result (of the election) been in any doubt."

London's FTSE rose 0.6% in a second day of solid gains and as MSCI's main global index notched its latest record, while sterling crept up to $1.2760 having risen almost 4% against the dollar and 2.2% against the euro since April.

Across the English Channel, polls suggested the National Rally (RN) would not win a majority of seats in Sunday's French election as mainstream parties moved to block the far right.

France's bond yields, which move inverse to price and are a proxy for government borrowing costs, were just edging higher though as investors eyed what could be a testing 10.5 billion euros ($11.33 billion) French bond sale later.

HOT CHIPS

There had been more record highs on Wall Street on Wednesday as Nvidia leapt another 4.5% and Asia-Pacific shares had risen nearly 1% overnight to reach their highest since April 2022.

Japan's Nikkei climbed 0.8% to within spitting distance of its March peak, while the broader Topix clinched all-time highs.

Taiwan's main index also struck a record led by the tech sector and Taiwan Semiconductor Manufacturing Co (TSMC) cleared T$1,000 for the first time.

The U.S. ISM measure of services activity surprised by sliding to its lowest since mid-2020, with employment notably weak ahead of the June payrolls report due on Friday.

Analysts cautioned the series was contradicted by strength in the PMI survey of services, but did note that price measures in both surveys pointed to easing inflation.

SURPRISE, SURPRISE

A run of subdued data mean Citi's U.S. economic surprise index has sunk to -47.5, the lowest since August 2022. Meanwhile, the closely watched Atlanta Fed's GDPNow estimate fell to just 1.5% from 1.7%.

That should be music to the ears of the Federal Reserve, with minutes of its last meeting showing committee members wanted more evidence of a cooling economy before cutting rates.

At the time of that meeting, the GDPNow growth estimate was running around 3% annualised.

"Reading through the minutes from only three weeks ago, it is a good reminder of how quickly the activity outlook has deteriorated," said Paul Ashworth, chief North America economist at Capital Economics.

"Given the more encouraging personal consumption expenditure data in May, the risk of a reacceleration in inflation seems even less likely, particularly with GDP growth now running well below its potential," he added. "We still think that the Fed will begin to cut interest rates this September."

Markets quickly lifted the probability of a September rate cut to 74%, from 65%, while pricing in 47 basis points of easing for this year.

With the U.S. economy now seemingly less exceptional, the dollar dropped across the board. The euro was up at $1.0797 , and away from its recent low of $1.0666, while the dollar index hit its lowest in three weeks.

The Australian dollar was a notable gainer, touching a six-month peak of $0.6733 as markets are wagering the next move in local rates could be higher.

The yen remained out in the cold, hitting multi-year lows on a host of currencies as investors continued to favour carry trades. The dollar stood at 161.53 yen after striking a 38-year top of 161.96 on Wednesday.

The drop in the dollar was a boon for commodities, with gold rallying to $2,358 an ounce, from $2,318 at the start of the week.

Oil prices eased a touch, having gained the previous day when a surprisingly large decline in U.S. crude stocks pointed to firmer demand as the U.S. driving season gets underway.

Brent dipped 73 cents to $86.62 a barrel, while U.S. crude fell 82 cents to $83.03 per barrel.

(Reporting by Marc Jones; Editing by Anil D'Silva)