I feel police on the streets should stop and ask suspicious people for ID's to see if they are legal if not they should be sent home ASAP , simple as that , i see many people which i know are ilegal but they stay in UK, if i was a police man i would ask them passport plz ...
I shall oppose to such method. It is practicized widely in Russia but the result is only the corruption of patrol police. Nothing more.
I'm sure such ilegals are most vulnerable in places they live. If you controle residential sector, every street every house, sooner or later you will clean all the country. Look, police patrol will never be punished he didn't arrest an ilegal. Nobody knows there was such meeting. But if you are a landlord or any irregular home police officer, it is always easier to prove you have given a shelter to suspicious persons or at least haven't notice smth evident