NCCPE, Wellcome Trust and BIS are conducting a review of funding schemes for Public Engagement in STEM. As part of their scoping activity, they have produced a handy list of current schemes:
www.publicengagement.ac.uk/sites/default/files/publication/national_forum_scheme_funding_summary.pdf

And here are some details about some forthcoming schemes:

Pathology: Public Engagement Innovation Grant Scheme: Deadline 8 June
The PE Innovation Grant Scheme was introduced to give financial support for the delivery of a range of pathology-related events throughout the UK. Grants of up to £1000 are available for individuals or organisations who wish to develop pathology-related public engagement activities or events.
www.ilovepathology.org/events/event-funding/grant-scheme

Wellcome Trust ISSF Public Engagement Funding: Deadline 26 June 2015
The University has been awarded a Wellcome Trust Institutional Strategic Support Fund (ISSF) to support a portfolio of biomedical research activities that harmonises with our research strategy and provides added value to our research activities. The scheme is open to staff and postgraduate students across the University for Public Engagement and outreach projects around the general theme of biomedical research and health. Collaborations across disciplines is encouraged.
www.intranet.ls.manchester.ac.uk/finance/funding/wtissf.aspx

Science Communication Awards 2015: Deadline 30 June
If you’re a bioscience researcher at a UK university or institute and involved in science communication – apply for the Society of Biology Science Communication Awards. The Awards are intended to reward outreach work carried out by both young scientists and established researchers to inform, enthuse and engage the public.
www.societyofbiology.org/get-involved/awards-and-competitions/science-communication-awards

Wellcome Trust Arts Awards up to £40,000: Deadline 7 August
The Arts Awards provide grants to projects that engage the public with biomedical science through the arts. The aim of the awards is to support arts projects that reach new audiences which may not traditionally be interested in science and provide new ways of thinking about the social, cultural and ethical issues around contemporary science. The small grants programme offers funding of up to £40,000; the deadline is the 7 August
www.wellcome.ac.uk/Funding/Public-engagement/Funding-schemes/Arts-Awards/index.htm

British Ecological Society outreach grants: Deadline September
The British Ecological Society is offering grants of up to £2,000 to promote ecological science to a wide audience. The funding is available for projects that: Increase public understanding of, and engagement with ecology; stimulate discussion about ecology and its implications for society; inspire and enthuse people of all ages about the science of ecology, especially those not previously interested; develop skills in communicating the science of ecology.
www.britishecologicalsociety.org/grants-awards/outreach-grants/

Society for Microbiology Science education and outreach grants: Deadline 1 October
The Society for Microbiology provides grants to promote microbiology or to support developments likely to lead to an improvement in the teaching of any aspect of microbiology. Members of the Society can apply for grants up to £1,000 for educational outreach activities including: talks, workshops, broadcasts, activities at science festivals and audio-visual or computer-based packages, activities that take place as part of a National Science and Engineering Week event at the applicant’s place of work.
www.sgm.ac.uk/en/grants-prizes/education-outreach-funds.cfm/education-and-outreach-grants