There are residence requirements for research council funding for postgraduate research. These are based on the Education (Fees and Awards) (England) Regulations 2007 and subsequent amendments.
Normally to be eligible for a full award a student must have no restrictions on how long they can stay in the UK and have been ordinarily resident in the UK for at least 3 years prior to the start of the studentship (with some further constraint regarding residence for education).
For further information regarding residence requirements, please see the regulations. These include further information, for example about refugees, migrant workers, residence for education and EEA nationals.
Fees only award
Students from EU countries other than the UK are generally eligible for a fees-only award. To be eligible for a fees-only award, a student must be ordinarily resident in a member state of the EU; in the same way as UK students must be ordinarily resident in the UK. Your eligibility for award will be determined on the basis of a fee status questionnaire issued by your institution.
For current students
If you have already started doctoral study, you may still be eligible for an AHRC studentship funding providing that, at the start of the AHRC award, you will have at least 50% of your period of study remaining.