(ShareCast News) - UK house price growth bounced back in May, according to official figures, with average house prices increasing by 0.9% over the month after a fall the month before.While simultaneously released data showed the country's core inflation sank back to 0%, house price inflation increased by 5.7% in the year to May 2015, according to the Office for National Statistics (ONS), up from 5.5% in the year to April 2015 that represented a 16-month low.Mortgage lenders also report modest rise in mortgage advances in May. The Council for Mortgage Lenders added: "House purchase lending in May was slightly up on the previous month, suggesting the market might be waking up after a subdued first quarter."ONS, which calculates its monthly release based on mix-adjusted average house prices and house price indices for the UK using mortgage-financed transactions collected via the regulated mortgage survey by the Council of Mortgage Lenders, said the pace of annual house price growth increased slightly across the majority of the UK in May 2015.House price annual inflation was 5.8% in England, 2.5% in Wales, 2.9% in Scotland and 10.5% in Northern Ireland. Figures on core UK inflation, also released by ONS on Tuesday, showed this fell back to 0% from 0.1% the month before.Economist Howard Archer said he felt this showed housing market activity was on the up, leading to expect house prices to rise by 6% in 2015, with upside risk coming from the current lack of properties coming on to the market. "There are increasing signs that housing market activity is now on the up; and we suspect that housing market activity will continue to improve amid generally supportive fundamentals and reduced uncertainty following the decisive general election result," he said.Annual gains in house prices in England were driven by stronger increases in the East and the South East.Figures showed that the average London house prices bounced back to £503,000, though they were still below their £514,000 peak from last August.The ONS said that in May 2015, prices paid by first-time buyers were 5.1% higher on average than in May 2014. For owner-occupiers (existing owners), prices increased by 5.9% for the same period.Recent data from non-official figures has shown house prices in June rose.Building society Halifax reported last week that, according to its research, prices picked up in the last quarter after two successive falls, with an unexpected month-on-month surge in June that may hint at at an acceleration of the ONS's next round of figures. The Royal Institution of Chartered Surveyors (RICS) also last week said prices were growing at their fastest rate in almost a year.