Many research funders now require or encourage authors to make their work available through some form of Open Access. The conditions can vary considerably between funders and some will make additional funding available to facilitate Open Access. You should be able to find a funders policy on their website.
Research Councils UK are committed to providing access to research, this covers research from a number of research councils including:
AHRC - Art and Humanities Research Council
BBSRC - Biotechnology and Biological Sciences Research Council
EPSRC - Engineering and Physical Sciences Research Council
ESRC - Economic and Social Research Council
MRC - Medical Research Council
NERC - Natural Environment Research Council
STFC - Science and Technology Facilities Council
Authors in receipt of Horizon 2020 funding from the European Commission will need to make sure their publications are openly available acroding to the policy guidelines and may also need to make their Research Data available.