LONDON, July 3 (Reuters) - The pound fell against the dollar on Monday as the U.S. currency rebounded from a tumble late the previous week, while traders continued to grapple with what expectations of several more Bank of England rate hikes mean for the British currency.

Sterling was last down 0.18% at $1.2669, giving back some its 0.63% Friday gain after U.S. inflation data came in softer than expected, and sent the greenback lower across the board.

The pound was steady against the euro at 85.94 pence.

It ranked among the best performing currencies against the dollar in the first half of the year, gaining 4.8%, thanks to anticipation British interest rates would rise by more than many originally expected and stay higher for longer.

But analysts are now starting to wonder whether the positive impact of higher rates for the British currency has run its course.

“The outlook for sterling is a battle between relatively high yields and poor growth prospects,” said Paul Robson, head of G10 FX strategy at NatWest, in a note.

The pound is expected to maintain a large yield premium over the euro for the next three years, and increase its premium over the dollar, Robson said, but "the extent to which this supports sterling will depend on the collateral damage it causes on the UK economy."

British government borrowing costs, as reflected by two-year bond yields, have soared this year. Two-year gilts yield around 5.3%, having risen by 160 basis points so far this year, compared with a 53-bp rise in two-year Treasuries and a 56-bp rise in German Schatz yields.

It costs the UK government more to borrow over two years than it does the governments of Italy or Greece.

The rise in gilt yields is underpinned by expectations of further tightening by the Bank of England, which raised interest rates by half a point two weeks ago to 5%, and is expected by markets to deliver an identical increase when it meets in early August.

Money markets show traders believe UK rates will now not peak until almost mid-2024, when they could rise to as much as 6.20%.

A month ago, the expectation was for a peak, or terminal, rate of around 5.3% by the end of this year, with the first rate cut following a few months later, but as things stand right now, traders expect no rate cuts until August next year.

"This big jump in UK yields has seen the pound outperform against its peers, rising by 5% against the US dollar, and by as much as 13.5% against the Japanese yen," CMC Markets market strategist Michael Hewson said.

"While financial markets try to determine how many more rate hikes are coming, the next question is how long they will have to stay at current levels, and what happens when the deflation that is already being seen in the PPI numbers starts to manifest itself in the core inflation numbers," he said.

There has been a sharp drop-off in wholesale input prices that make up the producer price index (PPI) to an annual rate of 0.5% from a peak of 24.3% last June.

Speculators now hold the largest bullish position in sterling since April 2018, when holdings were at their highest since 2014, two years before the Brexit referendum.

Weekly data from the Commodity Futures Trading Commission on Friday showed net non-commercial market players held a long position in sterling worth $4.142 billion.

Simmering in the background for the pound is the crisis at Thames Water, Britain's biggest water supplier. The government is considering taking the company into temporary state ownership, as it struggles with a 14-billion pound ($17.7 billion) debt pile. ($1 = 0.7896 pounds)

(Reporting by Amanda Cooper and Alun John; Editing by Toby Chopra)