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It's all fine, pretty quiet.
The Q1 path past Millwall FC is quite isolated but there's always people about at commuting times.
Waterlink Way I don't take after dark... doesn't feel sketchy at all during daylight, but I assume it's very quiet at night, so seems a bit unwise. You can just go up and down Perry Hill instead.
I've got basically the same start and end point and have been honing my route for the last year or so to avoid busy roads and traffic lights. It's a bit longer but so, so much more pleasant and same time/quicker due to the lack of traffic and lights:
https://goo.gl/maps/qdsoTYxqktxiSRVv7
You can get from Beckenham to Bricklayers Arms before you hit a traffic light, and Waterlink Way / Q1 is pretty relaxing to cycle on.