Looks like demolition is due to start this month.
The site notice says it will be on March 17th, though the email correspondence on the Lewisham planning pages records the planning department saying:
Also, the site notice says demolition works are intended to start 17th March 2018 – this is a Sunday? The earliest date a valid application has been received is 27.02.19. Allowing the 28 day period we have in which to issue a decision, the earliest you could demolish would be 28th of March. Any earlier demolition would not be permitted under the relevant permitted development rights and would be unauthorised and potentially liable to enforcement action. The notice also has to be displayed for a period of 21 days beginning on the date an application (entire i.e. including demolition method statement) is submitted to the local planning authority. The notice therefore needs to be displayed until 20thth March.
The notice should be updated to be clear on these two aspects.
I guess it doesn’t matter so much when it starts, so long as the disruption is minimised.