The rise in prices came despite a pick up in supply, with more sellers putting their homes up for sale than at any time since August 2008.
Prices in April were on average 2.6% higher than in March, but the data which is not seasonally adjusted showed sharp disparities between regions and property type. London continued to lead the way, with an annual price rise of 9%.
"With weather disruptions out of the way, more sellers are coming to the market and they appear to be ignoring the uncertainties facing potential buyers," said Miles Shipside, Rightmove's commercial director.
"Prices are up, but so is choice, and the two are not happy bedfellows in the longer term."
House prices in Britain shed as much as a fifth of their value during 2008 but recouped almost half these losses in the second half of 2009, helped by record low official interest rates and tight supply.
Rightmove said the market was now approaching a pivotal point in terms of supply and demand, and prices could be vulnerable to downward pressure later in the year. - Reuters
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