Getting permission in writing is a can of worms. People don't like to sign things.
If you have the property owner's email address (and you already have his oral permission), send him an email saying something like "I plan on doing some metal detecting at (address) later this week. Just checking to be sure it's okay."
He will email you back "Sure," and you print this exchange out and keep it in your pocket.
If he doesn't have email, you have a stonger case if you know his name and tell the policeman, "Yes sir, a friend of mine named John Smith owns this property and I have his permission to detect here whenever I'm in the area. I have his phone number here if you'd like to call him."