Here's a thought, why not just ask your landlord?
Because that presumes the activity-in-question is something that "needs someone's permissions", to begin with. I mean, sure, if metal detecting inherently "needs people's permissions", then your premise is correct. But if one doesn't start out with that mindset, then no, it doesn't need "people's permission". If you start with the assumption that metal detecting is dangerous, damaging, etc.... then sure, you'd be correct. But if you start with the assumption that detecting is innocuous and harmless, then you'd come up different. For example: would you ask the landlord if you can do yoga in your living room? Or do crochette on your back porch. Probably not. Why? Because we all inherently recognize those things as harmless, innocuous, etc... Why then is detecting somehow considered evil, wrong, dangerous, hazardous, etc...?
I detected the apartment complex of the lawn where I lived once, and never thought twice about doing it (apartment's built in the late 1950s, so I found a few wheaties). The landlord lived across town, and only came by every week or so, to check on things. But quite honestly, even if he'd driven up right while I was in the front yard, I doubt he'd have cared less. But sure, use common sense: If your landlord is an eccentric or somehow odd or something, then sure, ...... a little common sense is in order. I think anyone who's lived some place more than a month or two, knows a general feel for the liberties at whatever-place-he-lives in, the personality of his neighbors, landlord, etc....