Dave,
I cycle from Bromley to Bond Street, so pretty much the route you would be taking I guess. Main route for me is through Downham/Catford/Lewisham (A21) /New Cross(A20)/Peckham/Camberwell Green/ (A202) Oval/Vauxhall Bridge /Victoria/Green Park (always say good morning to Her Majesty as i ride past, she waves at me from her window

)
Relatively straight forward route, 12.5 miles takes me 50-55 mins. If you are coming from Bickley or Bickerley

, probably need to add 2 or 3 more miles to the distance.