South east london VFR flight - advice required

[Emkay]

I want to fly a local VFR route as follows:

http://s23.postimg.org/591pkqii3/Big...eds_castle.png

What would be the safest way to fly this route, in terms of the different ATSUs I should contact?

Is biggin approach likely to keep a hold of me or would they recommend I contact rochester information or london information when out to the east?

Note I already have an idea on what I should do, thought would like to see how other more experienced pilots would approach it