A definition of sustainable development:

Education for sustainable development enables pupils to develop the knowledge, skills, understanding and values to participate in decisions about the way we do things individually and collectively, both locally and globally, that will improve the quality of life now without damaging the planet for the future. There are opportunities for pupils to develop their understanding of sustainable development within the school curriculum, in particular in their work in Geography, Science, PHSE and Citizenship.
(page 23)

The Geography Orders for Key Stage 1 & 2 open with the statement that:
Geography is the focus within the curriculum for understanding and resolving issues about the environment and sustainable development.
(page 108)

This is made explicit in KS1 through these strands:
5a recognise changes in the environment
5b recognise how the environment may be improved and sustained

And at KS2 via:
5a recognise how people can improve the environment or damage it, and how decisions about places and environment affect the future quality of people's lives
5b recognise how and why people may seek to manage environments sustainably, and to identify opportunities for their own involvement

Breadth of study
6e … an environmental issue, caused by a change in an environment, and attempts to manage the environment sustainably.

The Science Orders for Key Stage 1 & 2 recognise the importance of science in that children:
... learn to question and discuss science-based issues that may affect their own lives, the direction of society and the future of the world.
(page 76)

This is made explicit in KS1 through:
Sc2 5c to care for the environment

And KS2 through:
Sc2 5a about ways in which living things and the environment need protection

The PHSE and Citizenship Orders recognise the role played in this area in preparing to play an active role as citizens.

At KS1 through:
2g pupils should be taught what improves and harms their local, natural and built environments and about some of the ways people look after them

And at KS2 through:
2j that resources can be allocated in different ways and that these economic choices affect individuals, communities and the sustainability of the environment

Breadth of Study

KS1
5g consider social and moral dilemmas that they come across in everyday life (for example simple environmental issues)

KS2
5a take responsibility (for example, for planning and looking after the school environment)

The issue of sustainability can also be highlighted through elements of the
DT Orders, for example at KS2:

3c recognise that the quality of a product depends on how well it is made and how well it meets its intended purpose (for example, how well products meet social, economic and environmental considerations)