I personally would close our borders to all immigration including those from the EU. Send back those that here legally or illegally, if they do not contribute to our society by being gainfully employed and paying taxes. The level of expenditure on the NHS, Education and Benefits would be considerably reduced. 
Now that's common sense
not the crap from some overpaid tossers in a government think tank. 
How would you police that? Uk passport holders only? Passport holders and family? Only retired age ? Stop Uk passport holders who have lived abroad for a few years from coming back?. Colour test?
How would you "find" those in the UK illegally? The border control folk cannot even find those released from Prison that should leave the country.

How would you "find" those in the UK illegally
By ensuring that any such agency charged with this responsibility was led by people intent on doing a thorough professional job rather than positioning themselves for a large salary, or a 'performance' related bonus, or a favourable remuneration upon termination, or an attractive pension, or a national award or some other such trivial piece of state recognition for supposedly doing a job ‘well done’.
The frustratingly impressive thing about all of the foregoing is that such activity has been performed by these people while still ensuring that their respective arses were covered to the degree where no amount of poor decision making, failing to suitably discharge their duties in an appropriate manner or any level of rank incompetence would ever impinge on their ability to hold (and continue to hold) these posts.
Accepting such poor performance now seems to be the norm in this nation and whatever else some others may think, the fault lies very firmly with those within at the Palace of Westminster, the established Civil Service, the hangers-on and doyens of the plethora of QUANGO’s presently blighting this country and, finally, within every council chamber across this country.
We are now reaping what has been sown as a result of the disinterest and a fundamental disconnect from any form of practical reality that has been, and is presently being, demonstrated by many people in this land.
Eyethangyew.