I can't recall the case law right now - sorry I don't have time to look it up, and you probably don't need it anyway as public sector HR is well aware of it! - but it is very, very unlikely that they will move to dismiss before your full sick pay entitlement runs out. There was a case several years ago where an employer dismissed on ill-health grounds before contractual sick pay ran out, and the employer lost because it was deemed that they had subverted their terms of employment unfairly - effectively, if you offer a term you must adhere to delivering that term.
What is very possible - and many public sector employers are doing this - is a two pronged approach:
Worst case scenario, they will start sickness absence processes (often at the six months mark) so that they can complete all the processes and "care elements" before you recah the 12 months. They may then either serve notice sometime in the half pay period (depending on how long your notice is, so effcetively saying "come back before your half pay runs out or you will have no job when it does") or wait until your sick pay runs out and serve you notice then.
Best case scenario is that they will start the above processes but wait until you run out of sick pay - but that is getting increasingly less common in my experience. My employer has just advised managers that we need to be shifting people off long term sickness "one way or the other".
Much as I hate this, I can get the point. With the best will in the world, and being entirely sympathetic to people who are off sick long term, we have no cover for them and are issuing potential redundancy notices to people who are in work.
It's difficult without knowing a bit more about the circumstances, but the end of January is several weeks away, and if you can't be sure that you can return then - is the issue work related or personal? And what do you think needs to happen to be able to go back to work? Because there are many options to support people that may be available, but, with respect, sitting at home worrying about when they will dismiss you is a self-fulfilling prophecy - you will make your anxiety and depression worse, won't be able to go back and will be dismissed. The employer has a responsibility to look at how they can assist you to return to work. But it isn't all on them - you need to look at what you can do, and what you might need, to be able to go back.
The longer you sit at home stressing about this, the more likely that you'll never feel able to go back. And that doesn't just affect this role - it is about, if you lose your job, how you then get back into employment and what a lengthy period of sickness does to your employment record.
There are things that people could advise you about - but not based on so little information.