There are actually two possible sources of funding to try to persuade certain people to return home. In some cases funding is provided directly by the British Government. That, for example, applies to people who've been released from prison:
http://www.timesonlin...cs/article3486104.ece
However, in most cases, funding is more likely to be provided by the International Organisation for Migration, which is a well-respected intergovernmental organisation, working throughout the world:
http://www.iom.int/jahia/jsp/index.jsp
In the UK 80% of the IOM's funding is from the British Government:
http://www.timesonlin...cs/article3056712.ece
Chris