There are certain flights that must start and finish from a licenced airfield, but these are PPL training flights. You don't need a licenced airfield if you already have a licence yourself!
When an airfield is closed, it is more than just removing the licence, basically the "owner" is removing permission to land on their property, so don't do it without having sorted something out in the first place.
However, landing at an unlicenced field should have no effect on your insurance unless for some reason this is mentioned, but I've never seen that.
DB, as a matter of courtesy you should contact any airfield you intend to land at, I do this as a matter of course even at larger airports, where you can PPR over the radio usually.
As for taking a light a/c into Heathrow!!! Unless you have a major problem and Heathrow is the only option, you have more chance of dating Pamela Anderson!
Basically though, within reason you can land anywhere you have the land owners permission, this can include a field, though this isn't recommended unless you know what you are doing, have recced it properly first and have a suitable machine (140hp cherokees aren't recommended!), but unfortunately too many people stick only to the "normal" destinations instead of going to wherever they fancy.
To me that's one of the joys and freedoms of flight rather than just going to the same old place for a crap bacon butty......