The Brexit deadline is getting closer and the rights of Estonians living in the UK and vice versa after Brexit remain somewhat unclear. Everything depends on reaching the actual deal and no one is seriously prepared yet for a no-deal scenario.
If a deal is made between the EU and the UK, everything will remain the same for the Estonians living in the UK and there shall be an additional transformation period until the end of 2020 when all new arrivals to the UK from the EU shall receive the same status as the EU nationals today. There will however be an obligation to re-register to get a "settled" status.
The same would apply for UK nationals living in Estonia (and other EU countries) but without the obligation of re-registering.
These chapters have already been written to the Brexit deal but if there is no consensus on all issues then there probably will not be any deal meaning the immigration issues could become extremely complicated. However, no one at the moment seems to believe in the worst case scenario so let us remain optimistic.