The Department for International Development (DFID) rebranded in 2009 as UKaid is the official bilateral development assistance agency of the UK Government. It has a range of funding opportunities for international as well as local NGOs in developing countries.
DFID announces several global opportunities to provide grants to civil society organizations around the world as well as within the UK. Major funding programs such as the Global Poverty Action Fund, UK Aid Match, Common Ground Initiative, Civil Society Challenge Fund and Programme Partnership Agreements (now closed) have been offering support to NGOs on long-term basis. In addition to these, there are also several call for proposals announced locally within various countries of focus for local organization to apply and benefit from.
Some of the major DFID funding opportunities for local NGOs in various countries are also listed in its main website such as the following. The Rapid Funding Envelope for HIV/AIDS is a grant only for civil society organizations in Tanzania.
You can search for DFID opportunities in your country here.