LONDON, June 7 (Reuters) - The pound was headed for a fourth consecutive weekly gain against the dollar on Friday, its longest rally since March last year, as investors prepared for data on the health of the U.S. labour market that could shape the outlook for U.S. rates.

Sterling was unchanged at $1.2789 at 0915 GMT.

On a weekly basis, sterling is set for a rise of 0.4% and is around its highest since March, having topped $1.28 earlier in the week. But much of that rally has been the result of dollar weakness, rather than pound strength.

Against the euro, sterling has performed far more modestly recently. It is roughly flat against the single European currency, a day after the European Central Bank delivered its first rate cut in five years.

That said, the pound is not far off its strongest against the euro since October 2023, largely down to the expectation among investors that the Bank of England will not lower interest rates until later this year.

Money markets show traders currently believe UK rates could fall to around 4.82% by December, from 5.25% right now. ECB rates are now at 3.75% and are expected to fall by at least another quarter point, and possibly by half a point, by year-end.

Friday's session will be dominated by U.S. non-farm payrolls, which economists expect to have risen by 185,000 in May. Traders are currently pricing in two quarter-point rate cuts from the Federal Reserve this year, with the first most likely in September.

There is a slimmer chance of two UK rates this year, given that some metrics, such as wage growth and service-sector price pressures, are still well above the Bank of England's comfort zone, even if headline inflation has slowed substantially.

Next week brings data on UK economic growth and employment, which could offer investors a steer on what to expect from the BoE in the coming weeks.

Bad weather over April and May has weighed on metrics such as consumer spending, but other data points, such as business activity, are showing signs of weakness too.

"Of late much has been made of the wet weather, but for us the continued use of this ‘explanation’ is starting to wear thin, with signs of genuine weakness in demand here rather than merely attributable to the weather," Santander UK economist Gabriella Willis said.

"A quarter of tepid growth would probably be perfect for the BoE right now, 'not too hot, nor too cold', giving the BoE time without a sharp contraction in activity forcing its hand with early cuts and without strong demand reigniting more robust price-setting behaviour," she said.

(Reporting by Amanda Cooper; Editing by Kim Coghill)