I was once told by my mum that Fairlawn School was built on the site of the Burmah Oil Company.

Out of curiosity I just did a search on the internet and found that a patent was applied for in Dec 1937 by the Burmah Oil Company and a Mr Charles Robinson Scott Harley of "Fairlawn", Honor Oak Road, Forest Hill, London, SE23. The patent was for improvements in the refining of Paraffin Wax and was accepted on June 16th 1939.

Seems likely that it was the Burmah Oil Comapany building that was destroyed by the rocket strike in Honor Oak Road. I would guess it was sometime nearer the end of the war.