Marie-Curie Fellowship. These are very well paid Postdoctoral Fellowships. Several current and past members of the Department of Psychological and Behavioural Science (formerly Department of Social Psychology) have been Marie-Curie Fellows.

Royal Society Fellowships. These are somewhere between a postdoctoral and faculty position. You would be a completely independent researcher.

British Academy. Several options depending on your circumstances.

Leverhulme Trust. Early Career Fellowships fund 50% of your salary (the other 50% to be funded through the LSE).

Economic and Social Research Council (ESRC). Early Career researcher funding.

Axa Research Fund Post-doctoral Fellowships. €130,000 for an 18 to 24 month period in particular areas (check the website).