For public engagement and/or impact work:

• Your ‘home’ institution: Many UK universities offer training and/or funding to undertake public engagement/impact activities.  Especially if you hope to gain employment in the UK HEI sector (whether as an academic or in an administrative role), it is very much to your advantage to take up these opportunities.  A strong track record in public engagement as a doctoral student will significantly enhance your subsequent application for a research assistantship on a collaborative project in the UK (or for employment in many parts of the charitable sector).
• AHRC/ESRC: The research councils occasionally offer training and/or funding for public engagement activities.  Keep an eye on their websites for more information, and for contextual information on public engagement and impact more broadly: http://www.ahrc.ac.uk/Pages/Home.aspx and http://www.esrc.ac.uk/collaboration/knowledge-exchange/index.aspx ;
• NESTA: This UK charity seeks to enhance innovation across a range of public domains and at intervals provides funding for public engagement for which academics can apply. See http://www.nesta.org.uk/get-funding .