@Walter Hinteler,
Again, the UK will be outside the EU, so you won't have to change any immigration laws within the EU. The UK is a giant world economic power in and of itself, and it beneficial to neither the UK nor certainly the EU to slap full tariffs on the UK when it leaves, which will cut down trade somewhat between the two parties. If the UK was small, you could shrug it off. The UK economy is not small, and the EU will not be able to shrug it off easily. Nor should it.
The UK doesn't want the EU politically, it very likely will be able to take in a limited amount of EU immigrants, (and the EU will take in a limited amount of UK immigrants), in exchange for reduced tariffs between the two parties.
The EU would be smart to negotiate these issues.