For example, what about the people living in Europe, would they become immigrants since they won't have any legal paper to reside in the country? What about the companies, several banks are moving their offices outside The UK.
EU will treat all UK residents with respect. It is not their fault UK us leaving EU.
London was banking center of EU. There was also European agency for banking that was moved I believe to Paris. Many banks and other offices was in London simply because of this fact. Now that was moved is normal that they were also moved out.
They may wish to treat all UK residents with respect but they have to be mindful of their own residents and their rights. Spain is one of the most interesting countries. There are something like 1 million expats from the UK living in Spain (that's the official number, I suspect it's much more). Are they going to send them all back to the UK and flatten their own economy in the process?