The funding bodies in England, Scotland, Wales, and Northern Ireland, have all given reassurances to EU nationals about continuing student finance eligibility in light of the UK's referendum on leaving the EU. See Brexit: Impact on student finance.
It is our understanding that a number of universities are guaranteeing that fee status will not be reassessed for the duration of the course for those who started in 2016/17, even if the UK leaves the EU before their courses end, and students will continue to be charged the 'home'/EU rate rather than the higher non-EU rate. You should contact your institution directly to confirm its policy but there is clearly an intention and commitment from institutions to do whatever is in their power to enable as many EU students as possible to continue to study in the UK, in the future.
Students starting in 2017/18
The announcement on student finance that was made in England in October 2016 (see our link, above) also confirmed that EU nationals (and their family members) who start studying in 2017/18, and who are assessed as eligible for loans/grants, will be eligible for 'home' fee status for the duration of their study.
Scotland have confirmed that tuition fee support will be provided in the normal way which, we understand, will tie-in with 'home' fee status eligibility.
Students starting in 2018/19
In March 2017, Scotland confirmed that "EU nationals choosing to study in Scotland and enrolling in 2018-19 have been guaranteed free tuition for the duration of their entire course". Again, we understand that this will tie-in with 'home' fee status eligibility.
UKCISA priorities and concerns over Brexit