Around 37,080 new homes were started between October and December 2015, up 23% on a year earlier, while 37,230 were completed, marking a 22% increase on the same quarter in 2014.
The latest totals were the highest since 2008, according to the Department for Communities and Local Government (DCLG), which released the figures.
There were 143,560 housing starts in the 12 months to December 2015, a figure which was up by 6% on the year before.
And 142,890 home builds were completed in the 12 months to December 2015, marking a 21% upswing compared with the previous 12 months.
The DCLG said there are strong areas of new build starts in parts of London, particularly in Newham.
Areas north of the London green belt in Cambridgeshire, Northamptonshire and Leicestershire have also been seeing relatively high levels of starts, along with areas in north Oxfordshire and the Thames estuary.
The report said the highest housebuilding completion rates are found in a band starting to the north of the London green belt, running through Cambridgeshire, Bedfordshire, Northamptonshire and Leicestershire, with strong completion levels also around Devon and Gloucestershire in the South West.
Areas with the lowest completion rates include Kingston upon Thames, Southend-on-Sea and Gravesham, while completion rates are hotting up in London, Blackpool and Basildon, the report said.
Housing starts saw sustained growth in the early 2000s, but they hit a trough in 2009 as the economic downturn took hold, before starting to climb back upwards.
While the number of housing starts taking place is still 22% below a 2007 peak, it is around double the level taking place during the 2009 low point.
Shelter said housebuilding is still "nowhere near" the 250,000 new homes needed annually to tackle England's housing shortage.
Campbell Robb, chief executive of Shelter, said: "Any rise in housebuilding is good news, but not good enough when we're still only building a little over half the homes we need."
The figures were released as a separate report found that new home planning permissions across England have reached their highest levels since 2008.
The Housing Pipeline report, from the Home Builders Federation (HBF) and construction data firm Glenigan, found that permission was granted for 242,819 homes in the 12 months to October, marking the highest 12-month total since early 2008.
It said planning permission for 59,875 homes was granted in England during the third quarter of last year, up from 53,409 permissions in the corresponding quarter the previous year.
But the HBF said the industry is concerned about the time lag of permissions being turned into homes.
It said many of the homes identified in its report still have a significant part of the planning system to navigate before any construction work can start - a process that could still take two or three years.
Stewart Baseley, executive chairman of the HBF, said: "The industry's ability to increase output still further will largely be dictated by the rate at which planning permissions are granted.
"Whilst the overall increase in outline permissions is welcome, most of these still have to navigate the complexities of the planning system before they can be built. It is imperative we speed up the time it takes for applications to be processed to the point that builders can actually build if we are to deliver further increases in housing supply."
The Help to Buy scheme has helped to boost the housebuilding industry in recent years.
Further measures outlined by the Government to build more homes include planning reforms to support small builders and new legal duties on councils to help promote starter homes.
Housing minister Brandon Lewis said: "We've got the country building again, with starts nearly double the low point of 2009, and along with completions, hitting a seven-year high."
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