Adds detail throughout, analyst comments in paragraphs 6-8

LONDON, May 6 (Reuters) - British government bond yields fell on Wednesday as oil prices fell for the second day in a row on hopes the Iran war could end after U.S. President Donald Trump indicated a peace deal could be possible.

Yields on British gilts were down between 6-7 basis points across the maturity range in early trade on Wednesday. That was in contrast to moves on Tuesday, when 30-year gilt yields GB30YT=RR rose to their highest since 1998. They were down as much as 7 bps at 5.667% at 0759 GMT.

Wednesday's move was in line with drops in yields on German bunds and U.S. treasuries.

British bond prices have slumped since the start of the U.S.-Israeli war on Iran in late February, and fell further as an agreement to reopen the Strait of Hormuz did not materialise.

Traders are closely watching local elections taking place in Britain on Thursday which could add to the pressure ​on Prime Minister Keir Starmer and raise questions about the country's future fiscal policy if he is replaced as leader of the governing Labour Party.

"A disastrous showing from Labour could trigger a fresh wave of selling in UK debt should markets brace for an open revolt in the ranks and an unceremonious ousting of PM Starmer," said Matthew Ryan, head of market strategy at financial services firm Ebury.

"The biggest risk here is a lurch to the radical left under a new leader, which could raise the spectre of looser fiscal rules, additional tax hikes and unfunded spending commitments that bond vigilantes will refuse to tolerate."

But analysts from ING said they were not seeing "clear signs" investors were turning more wary of UK bonds because of political turmoil.

Financial markets were pricing in 60 bps of interest rate hikes, equivalent to between two and three quarter-point rises, by the Bank of England by the end of this year.