The UK left the EU on 31 January 2020, which The UK was then in a transition period until 31 December 2020.
If you were not living in the UK by this date, unfortunately, you will not be able to study at UoB Manchester at this time. If you were living in the UK before the end of the transition period, you will be able to continue to reside, study and work in the UK under the EU Settlement Scheme.
Please read more on eligibility for British Citizenship and EU settlement on the government website at https://www.gov.uk/british-citizenship.