The funding bodies in England, Scotland, Wales, and Northern Ireland, have all given reassurances to EU nationals about continuing student finance eligibility for those already on courses.
Following earlier decisions by the funding bodies for those starting in 2016/17, there have since been some further assurances for students:
Students starting in 2017/18
England confirmed that "EU students applying for a place at an English university or further education institution in the 2017 to 2018 academic year [that is, the current academic year] will continue to be eligible for student loans and grants - and will be for the duration of their course [...] even if the UK exits the [EU] during that period". See England's 2017/18 statement.
Wales made a similar statement to England, on its news page, entitled EU Nationals and Student Finance in Wales 11/10/2016. See Wales's 2017/18 statement.
Scotland confirmed that "eligible EU students will continue to have access to free tuition, including tuition fee support [...] and [SAAS] will provide funding in the normal way. These students will be eligible to apply for funding from SAAS for the duration of that course. This applies [...] to students starting a new course from 2017-18". The statement is no longer publicly available but see 'Swinney demands student immigration guarantee' at gov.scot.
Northern Ireland confirmed directly to us that it would follow England's approach; namely that "the rules applying to EU nationals, or their family members, who have applied for a place at university from this August 2017 to study a course which attracts student support are unchanged. [...] EU nationals, or their family members, who are assessed as eligible to receive grants and/ or loans [...] will then be eligible for the duration of their study on that course".
Students starting in 2018/19
England reconfirmed its position for 2016/17 and 2017/18 (as above), and also confirmed the same funding package for EU students commencing study in 2018/19. See England's 2018/19 statement.
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". See Scotland's 2018/19 online statement and Scotland's 2018/19 EU referendum guidance pdf.
Wales confirmed that "EU nationals who intend to begin studying in the academic year 2018/19 will be eligible for support from loans and grants" and that these students "will not have the terms of their funding changed if the UK leaves the EU during their studies". See Wales's 2018/19 statement.
Students starting in 2019/20
In February 2018, Scotland confirmed that it will "extend [its 2017/18 and 2018/19] commitment to the 2019/20 cohort [which] means that all eligible non-UK EU citizens who come to Scotland to study for an undergraduate higher education qualification in 2019/20 will benefit from free tuition". See Scotland's 2019/20 statement.
Brexit: Impact on fee status assessments