The Edinburgh Local Development Plan is the thing to read.
The relevant section
http://217.174.251.127/dev/plans/eclp/chap5.htm#OS1
It says:
Policy Os 1 - Open Space Protection
Proposals involving the loss of open space will not be permitted unless it is demonstrated that:
- there will be no significant impact on the quality or character of the local environment
- the open space is a small part of a larger area or of limited amenity or leisure value and there is a significant over-provision of open space serving the immediate area and
- the loss would not be detrimental to the wider network including its continuity or biodiversity value and either
- there will be a local benefit in allowing the development in terms of either alternative equivalent provision being made or improvement to an existing public park or other open space or
- the development is for a community purpose and the benefits to the local community outweigh the loss.
The policy seeks to protect all open spaces,
both public and privately owned, which contribute to the amenity of their surroundings and the city, which provide or are capable of providing for the recreational needs of residents and visitors or which are an integral part of the city’s landscape and townscape character and its biodiversity. Many of the open spaces identified on the Proposals Map are covered by more than one designation, depending on their environmental quality and value to the community. It will be more important to protect open spaces in the future, as the population of parts of the city increases and brings added pressure on existing resources. The Council will only consider limited releases of open space to development in exceptional circumstances, where the loss would not result in detriment to the overall network or provision in the locality, and there are compensatory circumstances, such as scope for improving the quality of provision elsewhere in the network. Amenity areas in housing which have been provided with no clear purpose or sense of ownership might be considered for development, especially if a more comprehensive redevelopment of a wider area is in prospect and the resulting open space would be smaller in area but better in quality and usefulness.
Policy Os 2 - Playing Fields Protection
In addition to the requirements of Policy Os 1, the loss of some or all of a playing field or sports pitch will be permitted only where one of the following circumstances applies:
- the proposed development is ancillary to the principal use of the site as a playing field
- the proposed development involves a minor part of a playing field and would not adversely affect the use or potential of the remainder for sport and training
- an alternative playing field is to be provided of at least equivalent sporting value in a no less convenient location, or existing provision is to be significantly improved to compensate for the loss
- the Council is satisfied that there is a clear excess of sports pitches to meet current and anticipated future demand in the area, and the site can be developed without detriment to the overall quality of provision.
Playing field provision must be considered as a city-wide resource and in terms of its contribution to local needs. The Council’s assessment of provision in the city as a whole has concluded that the amount of pitches,
whether or not in public ownership or publicly accessible, is equivalent to the need. However, about one third are substandard and would need to be improved. On this evaluation, the loss of pitches to development cannot be justified in principle. However, the loss might be acceptable if alternative equivalent provision is to be made in an equally convenient location. Development has been allowed where other pitches serving the local community are to be equipped with all-weather playing surfaces.