Have you advised the CWO about the medical condition (with supporting evidence from your GP), which requires you to be in accommodation which you could not normally rent based on your income? If evidence is provided, the CWO may be able to make a case for you (not guaranteed, but worth a try if you haven't already done so).
The other point is that if the house isn't in a great state, it may not be suitable for your needs, based on your medical condition, which could help in a request for Rent Supplement above the stated limits.