Brexit will be effective on 01/01/2021 to go to London and other major cities of England, Scotland and Wales
Good news for now!
Here is the official website of the British government:
There will be no change to the rights and status of EU citizens currently living in the UK until 30 June 2021, or 31 December 2020 if the UK leaves the EU without a deal. You and your family can apply to the EU Settlement Scheme to continue living in the UK. https://www.gov.uk/legal-right-work-uk
If the UK leaves the EU without agreement
If you are an Irish citizen, you can enter the UK without a visa, as you can now. You will be able to work or study while you are here.
You can enter the UK without a visa if you are a citizen of another EU or EEA country, or Switzerland. You will be able to work or study while you are here.
The government proposes to end the free circulation, but that it still has to be approved by Parliament. Once free movement is over, you are a citizen of another EU or EEA country, or Switzerland, you can still enter the UK without a visa, but only for a maximum period of 3 months