It would say it's something wrong with the sax that's not obvious then.
Check the octave keys are operating properly. Check all the pads - one may be loose. It's unlikely to wear in the pads if it's happened suddenly. I had a similar problem the other day. It turned out to be a piece of fluff stuck to one of the pads, preventing it from closing properly. Have you tried different reeds? Make sure you haven't left something in the sax - pull through or strap or something (I did a whole gig once with a strap in the sax - thought it sounded a bit muffled).
Thanks for those suggestions, Nick. I did check the octave mechanism - seemed OK - and looked for small, furry animals asleep in the bell (that's what it felt like). I will check the pads more closely and look for bits of fluff etc.
I checked all the points suggested (except having someone else press down the pads, which I will do tonight) and they were ok. The effect didn't seem so extreme last night, so I'm wondering if some of it isn't due to the reed, which I had changed. I'll keep on checking, though.
get a flashlight, go in a dark room. put the flashlight in the bell and try pressing the keys to see if you see light escaping when the pads are closed. If this does not work, see a repairman who has a light designed for this. I would think he would check it for free in hopes of getting the repair work. A nastier easy way to check: If you smoke or know someone who does, have the person get a mouthful of smoke and blow it into the top of your horn where the gooseneck plugs in, while you press down all the keys. Smoke will be escaping from your problem area.