English UK, the national association of accredited ELT providers in the UK has provided some information & guidance about how Brexit will affect travel to the UK.
From 30 March 2019 until the end of 2020
There will be very few changes for students travelling to the UK after Friday 29 March 2019 until December 2020. During this time, anyone from the EU or EEA can enter the UK exactly as they do now (differences depend on whether the UK signs a deal with the EU).
If there is no deal, anyone who wants to stay for more than three months will have to apply online for a European Temporary Leave to Remain, which is valid for three years.
These will be accepted for entry to the UK until December 2020.
If there is no deal, ID cards will be accepted for entry until December 31 2020. If there is a deal, there will be a “transition period” while laws are being changed and ID cards will be accepted until the end of 2020. This means there is plenty of time to plan for when passports become necessary in 2021.
For more information, please visit the English UK website.