How can an environmental scientist or engineer benefit the ministry of defence?

Some of the working places of environmental engineer:
* engineering consulting firms that design and construct air and water pollution-control systems,
* industries that need to treat their air or wastewater discharges,
* private and municipal agencies that supply drinking water,
* companies that treat and dispose of hazardous chemicals,
* companies that operate treatment facilities for municipalities or industries,
* government agencies that monitor and regulate waste discharges,
* universities that teach and conduct research on environmental control,
* private and government laboratories that develop the new generations of pollution-control systems,
* international agencies that transfer knowledge and technology to the developing world, and
* public-interest groups that advocate environmental protection.

The big area of help is at military bases. Bases are just cities own by the government. I'm answering this based on the USA. Look at your list which I reproduce here in a little different form:

* design and construct air and water pollution-control systems,
* need to treat their air or wastewater discharges,
* supply drinking water,
* treat and dispose of hazardous chemicals,
* operate treatment facilities
* monitor and regulate waste discharges,
* conduct research on environmental control,
* develop the new generations of pollution-control systems,
* agencies that transfer knowledge and technology to the developing world,

All of the above apply to large military bases. On a base the engineers have to serve in all those capacities.

* public-interest groups that advocate environmental protection.

Also, government military agencies fund research that looks at all aspects of the environment. This requires experts to oversee these projects, so even that last one is involved.

When you start talking overseas deployment you get into things like reconstructing facilities that have been destroyed.