UPDATE 1-Stronger April services output and Q1 GDP boost UK rate hike bets

(Adds reaction from economists and markets in paragraphs 5-7, BoE mortgage approvals) LONDON, June 29 (Reuters) - Britain's services sector gathered steam in April and first-quarter GDP growth was revised up, official data showed on Friday, raising hopes of a pick-up after a sluggish start to 2018 that has kept Bank of England interest rates on hold. Services output, which makes up four-fifths of Britain's economy, rose by 0.3 percent on the month in April, its fastest growth since November 2017. Services output was up 1.6 percent from April 2017, picking up speed from the first quarter when it grew at an annual rate of 1.2 percent, the Office for National Statistics said. Sterling rallied against the dollar and the euro after the data, and interest rate futures raised the implicit probability of an August rate rise by the BoE to 60 percent from 50 percent. Britain's economy as a whole grew 0.2 percent on a quarterly basis in the first three months of 2018, an unexpected upward revision from an initial estimate of 0.1 percent. The ONS said the construction sector had shrunk less than it first thought. "The barriers to an August rate rise have come down as a result of this release," Investec economist Philip Shaw said. "In terms of the dynamics of how Q2 growth is playing out, it looks better than previously." On the year, Q1 GDP growth was unchanged at 1.2 percent, its weakest annual growth rate since Q2 2012 and in line with earlier estimates from the ONS and a Reuters poll. During the early part of the year, Britain was hit by unusually icy weather, on top of a squeeze on consumers from inflation caused by a weak pound and many businesses' reluctance to invest while the terms of Britain's March 2019 exit from the European Union remain unclear. At the end of last year, Britain was the slowest-growing economy in the G7 group of rich nations; on Friday, the ONS revised 2017 growth down to 1.7 percent, its lowest since 2012. The Bank of England predicts gross domestic product (GDP) growth will pick up to 0.4 percent on a quarterly basis in the three months to the end of June, as the economy rebounds from February and March's snow. If the economy looks on course for this, most economists polled by Reuters expect the BoE to raise rates, for only the second time since the 2008 financial crisis, on Aug. 2 after its next rate meeting. The ONS releases second-quarter GDP data on Aug. 10. Official data for April industrial output and construction have been weak, but retail sales have been stronger and private-sector surveys point to some recovery in May and early June. May mortgage approvals data released by the BoE on Friday beat economists' expectations, though closely-watched consumer sentiment figures released overnight were lacklustre. Friday's ONS data also showed that Britain's current account deficit narrowed to 17.72 billion pounds ($23.33 billion), compared to economists' expectations that it would hold broadly steady at 18 billion pounds in the first three months of 2018. As a share of GDP, this amounts to 3.4 percent, its lowest in a year, though it is still high by international standards. On Wednesday, the BoE said Britain's current account deficit was the biggest in the G7 and made it vulnerable to a fall in foreign investors' appetite for British assets, which could lead to higher borrowing costs for businesses and households. ($1 = 0.7594 pounds)

(Editing by Kevin Liffey)