The British Academy offers three year Postdoctoral Fellowships.
The ESRC offers Postdoctoral Fellowships that provide funding for one year (full time) or up to two years (part time) so that Fellows can devote time to publishing or otherwise prepare for successfull academic careers. Additionally, the ESRC offers funding opportunities to new and early career researchers under the First Grants scheme.
The Leverhulme Trust offers Early Career Fellowships to provide career development opportunities for those who are at a relatively early stage in their academic careers but with a proven record of research. It is anticipated that a Fellowship will lead to a more permanent academic position. In addition, Philip Leverhulme Prizes are awarded to outstanding scholars or practitioners (usually under the age of 36) who have made a substantial and recognized contribution to their particular field of study, recognized at an international level, and whose future contributions are held to be of correspondingly high promise.
The British Research Council administers the Researcher Exchange Programme which offers postdoctoral researchers the opportunity to live and work in countries other than the UK, building networks and research links around the world.
The SISTER website maintains a page devoted to Fellowships, many of which are postdoctoral. The first listings are "incoming" fellowships, for researchers currently located outside the UK who wish to obtain a fellowship at a UK university. Later listings are devoted to "outgoing" fellowships, those for researchers who wish to work outside the UK.