Should my company be able to phone me on my work mobile if I'm home sick?
It depends on the circumstances of your illness, how many times they phone and whether they really need to speak to you at that point. Some firms have a positive approach to rehabilitation, and if you have been off for some time, they may want to see how they can best get you back into the workplace.
Alternatively, you may be off with a cold when an important piece of paperwork is needed for a meeting that day, and only you know where it is. In such circumstances, it may be reasonable for a colleague to call you. But that should be a one-off and not a persistent interruption as this will not help you get well and, if they need to contact you frequently, then there is something wrong with the way your company's work is organised.