The UK left the European Union (EU) on 31 January 2020 on the basis of a Withdrawal Agreement, negotiated between the UK and the EU. Under the terms of this agreement, we have entered a transition period which is due to last until 31 December 2020. During the transition period most things will remain unchanged, including freedom of movement (the right to live, work and study in the UK). If you intend to remain in the UK after 31 December 2020, you will need to apply for UK immigration permission under the EU Settlement Scheme, and will have until 30 June 2021 to apply.
The Settlement Scheme is not only for those who intend to settle in the UK after studying. It is immigration permission, which can lead to settlement, but does not have to be used to gain settlement. With permission under the scheme there will be no restrictions on study (where you study or what you study).
Students arriving in the UK after 1 January 2021 will need to apply for immigration permission under the immigration rules that are in place at the time, in order to live, work and study in the UK.
You can find more information/guidance about the impact of Brexit on students and the EU Settlement Scheme at the following links: