The plan will be justified by ministers as being the most environmentally friendly and sustainable way of dealing with the problem, even though it implies building on the Green Belt surrounding many urban areas. Such areas are meant to be kept free of development.
The argument in favour of extensions will be spelt out in official planning guidance for local councils published next month. Ministers in the Department of the Environment, Transport and the Regions believe they are the best way of finding room for a million or more new homes in England, which cannot be squeezed inside existing built-up areas, over the next 15 years.
The new communities will be well served by public transport, include industry and offices, and be large enough to support their own schools, shopping centres and leisure facilities. That implies urban areas with populations of 10,000 or more.
The Government wants to make a break with the pattern of the past, in which estates were tacked on to towns, creating low-density, car-dependent suburban sprawl.
It has also rejected large new self-contained settlements built in the open countryside, the idea that inspired the post-war new towns of which Stevenage in Hertfordshire was the first.
The new-style extensions will be within a few minutes' bus ride of a railway station. They will have a car-free "dedicated public transport corridor" linking them to their "parent" town and station, and networks of footpaths and cycle ways will dissaude residents from driving.
Two extensions have recently been approved by local councils - at Stevenage, which could add up to 10,000 extra homes, and a smaller one at Newcastle upon Tyne. Both will be built entirely on Green Belt land, which has had to de-designated, to the fury of local residents.
At Prince Charles's Poundbury extension of Dorchester, Dorset, 140 homes have been completed on Duchy of Cornwall land - but it will eventually grow to nearly 2,000.
The extension has been built at much higher densities than most post- war suburbia, with front doors opening directly on to streets. Yet it has proved highly popular. MPs on the Environment Select Committee have visited and reported that Poundbury was a model for housing of the future.
Roger Higman of Friends of the Earth said: ``Before the Government approves extensions, it needs to do much more to encourage development and regeneration within cities and reduce building on green fields.''
Neil Sinden of the Council for the Protection of Rural England said ministers' first priority should be to make the planning process more flexible and attuned to what local people want, rather than providing a stream of greenfield sites.
The hope is that developers will finance regeneration and improvements in the old towns in return for planning permission to build the extensions.