If you are keen for English Heritage to list it then I suggest that you contact them directly. I think this is something you can do from their website. Alternatively it might be worth a conversation with the Conservation Officer at Lewisham, who may not be aware of the buildings 'local importance'.
Alternatively we can suggest that it is a non-designated heritage asset (i.e. an important building that is not formally listed but that has heritage value). I think we will need more information on its history, previous uses and design to do this.
Is this information that anyone has access to e.g. old photo's, information about original uses etc etc. ?