I`m currently doing a PhD in Psychology (self-funded) at the University of Gloucestershire. I have a BSc (2ii),MSc and an ESRC recognised MSc. However, ESRC say that my department is not ESRC recognised and funding cannot be obtained. I wonder if they mean the quota system, as I want to apply for the +3 studentship competition instead.

Not all ESRC recognised departments receive quotas and not all departments are recognised. The ESRC states of the +3 studentships that:

"...applicants will apply through a recognised outlet which holds either 1+3 or +3 recognition"

Ask in your department, they will know if they are an ESRC recognised outlet or not.