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The City Plan 2030, published today, also calls for new developments to be a mix of residential and other uses, creating 20-minute neighbourhoods with services closer to where people live.
It proposes a new minimum of 35 per cent affordable housing in any new development instead of the current 25 per cent.
And new homes would have to be net carbon zero when they are built.
Planning convener Neil Gardiner said he wanted to recalibrate how development happened in the city.
He said: "Rather than growing forever outwards, the proposed plan focuses on developing new communities on brownfield land which mix living, working and leisure uses."
It means council leaders have opted not to put forward areas of the greenbelt which had been mooted for potential development, including sites in Kirkliston; West Edinburgh near Glasgow Road; South-East Edinburgh, around Gilmerton; part of the so-called Garden District, east of Riccarton; and Calderwood, near the Jupiter Artland sculpture park.
A new mixed-use neighbourhood is proposed in West Edinburgh, using a combination of sites near the airport, which would be based around existing infrastructure, with the tram running through and the Edinburgh Gateway train station nearby. The land was previously designated largely for business development.
New neighbourhoods on brownfield land at the Waterfront will also be taken forward.
And other brownfield sites designated for new developments include Seafield, Redford Barracks, Astley Ainslie, Edinburgh BioQuarter, Liberton Hospital, Bonnington and Fettes.
The City Plan is based on a target of having enough land – including sites already allocated – to build 37,000 new homes but the council says the proposed sites and existing sites are together enough for more than 57,000.
The council acknowledges the proposals will be challenged by developers and landowners eager for greenbelt sites to be made available for housing, but it says it will robustly defend the need to shift towards brownfield.
Councillor Gardiner said: "There is sufficient land in the city. Climate change is not going away and that signals the need to do things differently, so the whole idea of forever building outwards and driving into the city can't really work any more. Our roads are crowded as they are.
"It just requires developers to think a bit differently. And we are already seeing that happening – there have been a lot of applications in the last couple of years in the Bonnington area, for example, with hundreds of houses getting approval and being built."
He said developing urban sites instead of going into the greenbelt meant existing infrastructure could be used and services were easier to deliver.
And he gave the example of the former council depot at Murrayfield, which was next to a public park, close to the new Wester Hailes healthy living centre, with investment being made in the new Wester Hailes high school; there were bus routes and it was not far to the tram. "It makes absolute sense to go for those sites – and it connects Wester Hailes to the rest of west Edinburgh, so there's a real social equality element to it as well as physical planning."
Councillor Gardiner said it was important to maintain Edinburgh’s green setting and not allow the city to spread all the way to Livingston.
"Land is a finite resource – once it’s gone it’s gone. We want to use our land sparingly and to its best advantage because it is some of the prime agricultural land in Scotland.”
Planning vice-convener Maureen Child said rather than having “houses parachuted into a greenfield area” the City Plan proposals invited developers to help build a sense of neighbourhood.
And City Plan programme director Iain McFarlane said the the 20-minute neighbourhood approach fitted with the traditional character of city – busy, mixed-use, high-density, “liveable” and “walkable” neighbourhoods.
“The areas so many people want to live in have that character and we should reproduce that for the future because it's intrinsic to the city. It is making new neighbourhoods that function like Bruntsfield does or Leith does, rather than just housing estate that don’t have services, facilities or good public transport.”
He said the proposed increase in the proportion of affordable housing in new developments was supported by studies on the levels of need for such housing, but also calculations showing developments would still be viable with that requirement.
And he said energy use was critical to the council’s ambition to be carbon neutral by 2030.
“We are proposing a policy which requires all new buildings, through fabric or low- and zero-carbon generating technologies, are carbon neutral in their built state.”
He said he was confident there would be developers keen to be involved in the council’s new approach.
"It’s not just about the five or six big volume housing developers, there are people out there interested in doing the kind of thing we're looking at, which is hugely encouraging because it's really important we get away from that low-density, car-based mono-use approach because it doesn't support good services or good public transport or active lifestyle.
"We can't afford to continue development in the pattern that has happened over the last 40 or 50 years in terms of climate change and sustainability.”
The planning committee will consider the proposed City Plan 2030 next week. Final representations will then be invited and considered by the council before the plan is submitted to the Scottish Government.