The ESRC's South Coast Doctoral Training Partnership (Southampton, Brighton, and Portsmouth) will fund at least 38 PhD students this year, on either a +3 (PhD) or 1+3 (MSc and PhD) basis. Some of these studentships will be for particular projects, advertised separately, but there's also an open call for student proposals here. Deadline end of January 2018.
I'm not directly involved in the ESRC funding
decisions, but I am Doctoral Programmes Director for Politics And