Recently the government produced its proposals for safeguarding the position of EU citizens living in the UK and UK Nationals living in the EU. At last we have some idea about what Brexit will actually mean for EU citizens in the UK, but it's only an idea because the proposal has yet to be negotiated with the EU.
In essence the proposal is:
Nothing will change until the UK actually leaves the European Union.
EU citizens will be able to live and work in the UK in the same way.
After the UK leaves the EU, every EU citizen (and their family) will need to make sure that they have legal immigration status in the UK.
At the moment, EU citizens do not have to apply for confirmation that they are in the UK legally. This will change when we leave the EU. Employers, landlords, public services etc. will need to see evidence that an EU citizen is here legally.
There will be an important date - a cut off date somewhere between 29 March 2017 and the day the UK actually leaves the UK. If you are an EU citizen, your position will be decided by what you were doing at that date. This date has not been decided yet.
If you arrived in the UK before the cut off date and have lived here continuously for 5 years,
You can apply for settled status. This applies whether or not you hold a Permanent Residence Card. If the government sticks to this proposal, those with a card are likely to obtain settled status quickly and easily. (See below for settled status)
If you arrived in the UK before the cut off date and have not lived here continuously for 5 years,
You can also apply for settled status after you have been here for 5 years even if the UK leaves the EU during the 5 years.
If you arrived in the UK after the cut off date,
You can apply for a temporary residence permit but in the long term, you will have to apply to stay under the rules that currently apply to non-EEA residents of the UK.
This is the most secure immigration status you can obtain in the United Kingdom if you are not a British Citizen. If you are settled, you are free to live in the UK without conditions (e.g that you work, study, look for work or be self-sufficient). You can access public funds and services and apply for British Citizenship. You lose settled status if you leave the UK for a continuous period of over two years or if you commit a very serious crime.
There will be a grace period after the UK leaves when EU citizens can still apply for permission to stay. All EU citizens who have not already applied for settlement will be in the UK legally during this period but this will end. If you have not obtained settled status or a temporary residence permit by the end of the grace period, you will be in the UK illegally.
If you are an EU citizen and you wish to stay in the UK after it leaves the EU, it is a good idea to make preparations before the UK actually leaves. There will be a grace period, after the UK leaves when EU citizens can apply for permission to stay but this period will end. If you have not obtained settled status or a temporary residence permit by that date, you will be in the UK illegally.
Remember this is just a proposal and may not be the final position. Here is a handy diagram from the government document: