Economic and Social Research Council (ESRC)
The ESRC provides the following fellowships:
Career development postdoctoral fellowships which fund researchers for one year immediately after completion of the doctorate (see under postgraduate funding on the ESRC website)
Longer postdoctoral fellowships for any stage in your postdoctoral career (see under research funding)
Medical Research Council (MRC)
The MRC provides fellowships for various stages in the academic career.
The Wellcome Trust provides fellowships for various stages in the academic career.
Max Planck Institute for Demographic Research, Rostock, Germany
The Max Planck Institute for Demographic Research frequently has fellowships/ jobs available for postgraduates and postdoctorates in demography.
The Nuffield Foundation has a New Career Development Fellowship Scheme.
The British Academy
The British Academy has postdoctoral fellowships (and demography is one of the categories they will potentially fund) as well as more senior research fellowships.
The Leverhulme Trust
The Leverhulme Trust awards Early Career Fellowships and Research Fellowships for more advanced researchers.