After more hours play: https://www.gog.com/forum/fallout_london/settlements_and_safe_stashes/post4

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Original post:

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Has anybody found a buildable settlement yet - or even a safe place to stash things?
I'm maybe six or seven hours in but nothing so far.
Maybe I've been wandering in the wrong directions? XD

Yeah i've found one, its the airport in the south, you have to do gordos? i think thats his name.. hes super hard to miss.. anywho you have to do his quest line which is just a few short quests.

Havent met anybody with a name like that! O___o

Still havent found anything to do with that guy - BUT...

London Bridge (NOT Tower Bridge! - it's next to the Ferryman's Dockhouse). WARNING! Settlers etc have a habit of falling through the bridge and drowning. DO NOT POPULATE WITH COMPANIONS!!!
Covent Garden
Lambeth Walk
and
A construction site south west of Lambeth Walk are all habitable.

Might be mission related (im leaving out spoilers).
So if you want to get building fairly quick, best i can suggest if following the main plot until you hit the ferryman's dockhouse.

Also I used the explosives box there as storage for a long time without issue. Its also where Churchill may end up when dismissed,

Edit: eventually found the "gordo" guy mentioned above. He's a distance south west of the swan and mitre. Not really on the trodden path.