It sounds as if a spring's become unhooked. Find the spring for the floppy key by folloing the arm back to the rod. See which side of the post it is, it's probably on the wrong side. Chances are you caught it cleaning. Just carefully move it back to the correct position, probably the other side of the post. Use the balde of a small screwdriver (carefully) or a small crochet hook (better).
Look at the needle spring associated with that floppy key. Has it popped out of its retainer or maybe even broken ?
If it has popped out, then it should be possible (but maybe a bit fiddly) to put it back in place. Look for the place near the sharp end (the free end that isn't fixed in a pillar) where the spring is supposed to be pushing against a metal post on the rod. There is usually a cradle or a groove where the spring should fit. Sometimes you can put a spring back with your finger (watch out for the sharp end) and sometimes you need to use a pushing device like a screwdriver, a proper spring hook or a crochet hook.
If it's a bust spring then I would take it to your repairman, but plenty of people do that repair themselves. It's only really tricky if the old spring is rusted in.
Thanks Kev and Rhys - I rang my regular repairman, he is enjoying the sunshine in spain presently - He informs me that there is an adjusting screw on the floppy key ( Its the first one on the bell ) I have never noticed it before, it most be unique to the Antiqua - But didn't think it would allow that much play!
Will try to adjust this when I get home from work.
Assuming it's not loose, it can be adjusted stronger by bending. But be careful, they break easily. But... Depending on which spring it is (your desciption isn't too clear), the octave mechanism may be involved. If the octave mechanism is involved, go to a technician.
Assuming the octave mechanism isn't involved, and it's not loose in the post, unhook it and increase the bend away from the post, but make sure you support it so there's no bending where it goes into the post. In Stephen Howard's sax manual he suggests using round nosed pliers and twisting the spring at many points along the length to get a smooth curve. The twist should be done so that it doesn't bend the spring at the post. You may need to do some dismantling to do this...
But... Why did the spring become weak? Assuming it was OK, something changed and you need to find out what it was. Anything bent/sticking? Missing cork(s)? Springs don't usually loose their tension. Could still be that you caught it cleaning, or on something else.
If you're unsure, take it to a technician! It'll probably be cheaper and a lot less hassle than breaking something.