Not so fast, CC.
If he's well enough to look for another job, he's well enough to be at work and doing some duties. A case for a written warning if I found him doing it.
It depends on what you are off work with. If the job is causing the illness then u are well within your rights to look for another job, just don't let your employer find out about it.
I don't think there is anything illegal but they may try and get you if your sickness should prevent you.
I have in the past got another job whilst off sick, the old boss didn't like it and gave me a rubbish reference and withheld my holiday pay.
But you can do it