I've conducted some primary research/intelligence gathering on this today.
This afternoon I went to see June at Chestnuts. She was Julie at Allure Maddison, Sydenham. (Review to follow later today in new post). Asked her for the details.
As you suspected, Allure Maddison has definitely closed down - after about 20 years. Apparently, a new residential neighbour complained about it to the estate agent below - which owns the flat it operated from - and the Allure owner decided to shut up shop rather than risk any trouble. It seems the original owner had passed away some time ago and the business passed to the next generation, which wasn't quite as into it anyway and this complaint made their mind up.
Apparently they have been considering a new premises, but in a fairly passive way so it may rise from the ashes, but there's nothing on the horizon at the moment.