I expect they want to divert people onto main roads and bus routes. However, by all accounts you can turn down Sydenham Rise and continue on to Honor Oak and Waldenshaw.
I assume they are not diverting people down Thorpewood Avenue either to avoid huge problems for residents. But with the diversions in place there are a series of short cuts for people who know exactly how to get through Forest Hill without passing Sainsburys.
It is a shame that, as with all such road works, they have not adjusted the traffic lights outside the station to take account of the fact that nobody is coming out of London Road.