I'm not confused at all, the "no demolition without design" was the first phase of a conservationist campaign whose second phase is called "Save the face of Forest Hill", they were started by the same person that submitted the application for listing and at the time of the petitions the application had already been submitted and at no time, until listed status was granted, people asked to sign were told about the application.

Confused is who thinks that converting Louise House into flats could bring in any money, let alone upholding Louise House for its services to the poor whilst proposing to sell it to the wealthy.

The SFFH petition is inconsistent with a petition altogether. Technically speaking the petitioners have no power to reject anything. A petition that's properly written asks somebody to do or not do something.
Unless you're claiming that the petition was not for the attention of the Mayor but of Tim Walder, imploring him to submit an application for listing of Louise House but that would be rather at odd with the fact that he started the petition and with the fact that there's no mention of listing in the petition text.

On consultations, again, they are not referenda, they are there to inform the people of what the Council is doing and to inform the Council of what the people think of it so that the Mayor can take fully "informed" decisions and I think he's got the picture of public opinion quite clear, what he doesn't know now is where the money is to come from.