For Students going to or coming from UK-base higher education institutions for study mobility:

The United Kingdom remains an EU Member State until 31 October 2019, with all rights and obligations. This means that the United Kingdom continues to participate fully in the Erasmus+ programme. Furthermore, in case the Withdrawal Agreement is ratified before 31 October 2019, the United Kingdom will continue to be eligible under the Erasmus+ programme. In case the United Kingdom withdraws from the Union without a withdrawal agreement, individual mobilities (Key Action 1) that are ongoing when the UK withdraws from the EU do not have to be interrupted, even in the no deal scenario.

Please, refer to the regularly updated Q&A site pf the Erasmus + Program for further information https://ec.europa.eu/programmes/erasmus-plus/about/brexit_en