Gary,
The short (but not very helpful) answer to your question is that it all depends...............
[All this relates to the UK]
Trying to be a bit more helpful but only summarising what is a minefield.............
1. Most landings require the landowners' permission BUT HEMS and police flying has special exemptions/permissions that allow them to land without specific permission of the landowner.
2. In general, a landing inside a congested area (not at a licensed field) needs to have specific permission from the CAA (cos otherwise it represents a breach of Rule 5 of the Rules of the Air). HOWEVER, there are a series of exemptions to this- police and HEMS can land without CAA specific permission, so long as they operate in accordance with set down procedures and limits (recorded in detail in Operations manuals etc.) In addtion, some commercial operators have a general permission to make such landings, that are controlled and recorded in a broadly similar way to those of the police/HEMS. They have to have a special section added to their Ops Manual that sets all these things down. You get this if you are trusted and experienced in such things.(These all apply only to multi-engine helicopters)
I'm getting bored now, but that is the general gist........
OH yes! Nearly forgot - the important thing is that whatever special rule applies the basic rule (Rule 5 again) that single engine failure should not put persons or proeprty at risk on the ground still applies, so it all has to be Group A/Category 1 etc. etc.