It would be sensible to talk to your doctor about this too so you can agree a phased return to that activity as well. This way should your employers question it you can say that you sought medical advice and you are following that advice. Your employer's concern is likely to be that by starting your own business again you are expending your energy on that and that it will delay your recovery and mean you return to them later than you otherwise would. As such it is best to meet this concern head on by getting your GP'Ss approval.
I hope this helps. If there are any further points please reply
Yes but I would specifically ask your GP to consider the point about whether it might delay your return to your employment. The answer will be no but you have ensured that you asked and can tell your employers this should the issue arise.