Yes, you can be signed off work indefinitely in cases where you don’t know when you are going to get better and there doesn’t seem to be a time limit on your medical or mental condition. To get signed off work indefinitely you might need to talk to your doctor and ask them about how long they consider necessary for you to get well or feel better.  In some cases you can also self-certify the first 7 days and after it, if you need to get signed off work indefinitely, you can get a sick note or fit note from your GP.