Radiator on plaster and lathe wall

[clueless]

We've just removed a single radiator from a plaster and lathe wall in our kitchen in order to decorate and discovered that it seems to be held on by almost nothing.

There are two metal brackets, each held on by four screws two of which don't seem to screw into anything at all. The other two screws seem to be gripping something, but there's movement in them.

The plaster is in generally poor condition and can be seen moving if you pull gently on the radiator.

The plaster is about 10 cm (4 inch) in front of an exterior wall.

What's the best thing to do to get this re-attached securely?

Thanks