They know that linking up with other schools around the world for joint projects, and teacher and pupil exchanges, broadens their outlook, and that of their pupils, and prepares those pupils for an increasingly global world.
But now the Government believes such activities should not just be bolted on, as occasional, optional events in the school calender that depend on the motivation of individual teachers. Instead, they should be part of the school ethos and embedded in the curriculum.
Schools that attain a high level of internationalism are already recognised by the British Council-run International School Awards, a kitemark achieved by some 120 schools this year.
At this year's awards ceremony, held in London last month, Charles Clarke said he was committing to extending and developing the scheme.
This is widely expected to form a part of the Secretary of State for Education's international strategy, to be announced at the start of International Education Week on Monday. "I think it's exceptionally important that we do what we can to try to get a much higher level of international awareness, engagement and participation in our schools," says Mr Clarke.
At present, to qualify for the award, schools draw up a dossier of the activities that they are carrying out with the help of the British Council and other bodies that organise international contacts - such as Teachers International Professional Development and the EU's Comenius programme.
If the school shows it has implemented such activities successfully it then becomes eligible for the award.
"It is a tough, high-quality process, and the award is a recognition of excellence," says Mary Stiasny, the British Council's director of education and training.
Five Indian schools also achieved the award, and Sweden and the US are interested in launching their own versions - an indication of the award's high standing internationally.
Mr Clarke is expected to further embed internationalism in schools by extending the award scheme to more schools and by providing new foundation and intermediate levels for schools to work towards before being given the final award.
Each stage would have its own criteria - but the award itself would retain its rigour, says Stiasny. "There are a lot more schools out there doing international work who are not seeking recognition for it in any way. This would bring them in."
The idea is that some 7,000 schools could be involved within three years, at least at the foundation stage of the award, while the hope is to cover all schools by the end of the decade.
New funding for the international awards is on its way. At the award ceremony, Clarke announced an additional pound;250,000, bringing to pound;475,000 the total amount of money available for developing, promoting and managing the scheme, and also for running the awarding panel that evaluates the schools.
Yojana Sharma International education week: www.teachernet.gov.ukeducationovervieweventsiewBackwell primary receives an International School Award, see page 15