The typical home in the East increased in cost by 8.3% in the year to the end of July, the Office for National Statistics (ONS) said.
Prices in London, which saw big rises last year, rose by 5.5%, slightly lower than the average in England of 5.6%.
Overall, UK house prices increased by 5.2% in the year to the end of July.
The other area to see significant price growth was Northern Ireland, up 7.4%.
Property values in Northern Ireland are recovering from a massive fall during the financial crisis, and remain 42% below the peak of August 2007, the ONS figures show,
Prices rose by 6.7% in the South East of England, the ONS figures show, although here - as in the East and in seven other regions - the pace of price rises has slowed.
Analysts suggest that the time of double-digit price rises in London is over for now.
"There is very much a ripple effect - the action has moved out from prime central London to the outskirts and those commuter areas where there is better value to be had, although not as much if prices continue to rise as they have been," said Jonathan Adams, director of central London estate agency Napier Watt.
The 5.2% average price increase in the UK was down from the 5.7% rate recorded in the previous month. Prices in Scotland fell by 1.3% and were 0.7% lower in the North East of England.
Excluding London and the South East of England, UK house prices increased by 4.4%.
The average home cost £295,000 in England, £173,000 in Wales, £154,000 in Northern Ireland and £196,000 in Scotland. In England, the highest average price was paid in London (£525,000) and the lowest in the North East (£156,000).
The average price paid in the UK was £282,000, and analysts expect this to continue to rise, not least as a result of a lack of properties in the market.
Writing in the Guardian, Neal Hudson, a housing market analyst for Savills, said that the cost of buying a property, rather than the cost of owning it, is the biggest barrier to people buying their first home. That is because a large amount is needed for a deposit, while mortgage costs are well below the norm.
Figures from the Council of Mortgage Lenders show that the number of homeowners remortgaging - in order to take advantage of low rates - rose by 26% in July compared with the same month a year earlier.
House prices are rising fastest in the East of England, official figures show, as analysts suggest property market "action" has moved out of London.