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.

The Eide Barge 33 missed the Valhall field by at least 1km (0.6 miles).
More than 300 oil workers were airlifted from the Norwegian sector of the North Sea after the high winds broke the barge's anchor.
Stormy weather in the area has seen waves topping 15m (50ft).
A man died when a huge wave hit another rig earlier in the Troll field off Norway.
The strong winds tore the barge from its moorings and sent it towards BP's Valhall platform, located in the middle of the North Sea between Norway and the UK.
The oil and gas company was forced to shut down output and evacuate staff on board. ConocoPhillips also stopped production and evacuated crew from installations in the same area.
A spokeswoman for the Rescue Coordination Centre for southern Norway told the Reuters news agency that the danger posed by the barge was now over.
"There are no other installations between the barge and the coast of Norway," Borghild Eldoen said.
"It is now up to the owners of the barge to stop it before it reaches the coast."
At one point fears about a collision increased when the barge - 110m in length and 30m wide - changed course and headed straight for Valhall, BP  Norway spokesman Jan Erik Geirmo told the AFP news agency.
But in the event it floated away from the evacuated platforms.
Mr Geirmo said that a tug had been deployed to immobilise it - an operation which will be dangerous in such stormy conditions. He said the situation was now returning to normal and employees will progressively return to the platforms.
Norwegian media said the barge ran adrift on Wednesday evening some 25km (15 miles) from Valhall.
House prices are rising fastest in the East of England, official figures show, as analysts suggest property market "action" has moved out of London.
[NEXT_CONCEPT]
A potential major disaster in the North Sea has been narrowly averted after a large, unmanned barge went adrift in stormy high seas and came close to colliding with offshore oil platforms.