House price inflation eased in June, with asking prices up by 0.3% on average down from a gain 0.7% in May as a wave of new houses came onto the market, according to property website Rightmove.Average asking prices are now £237,767 against £237,134 last month. The online agent estimates there was a 22% increase in sellers coming to the market in June following suspension of home information packs (HIPs), with a large chunk of these still unsold.The annual rate of inflation picked up from 4.3% to 5%, but Rightmove expects this to ease back as conditions get tougher later in the year.Sellers and tenants face tougher times as deficit reduction measures, such as rumoured CGT increases, disrupt the fragile housing recovery, it said.Rightmove's commercial director Miles Shipside added that a continued dearth of mortgage availability and a recent surge in sellers will also knock confidence."These factors are likely to put an end to this year's recovery in house prices," Shipside said.