Could anyone help me find some Greek script typefaces like these?
When I was young I studied classical Greek but the fonts used for classical texts were all quite sober.
I am particularly struck by the λ (as in γάλα), double λλ and η that looks like a cyrillic и (both in Ελληνικό) on the carton of milk.
Could anyone say how close this is to normal modern handwriting?
A Google search for Greek fonts will find some, but in a quick search of Font Squirrel I found only one that was not like most other formal fonts: VAG Handwritten.
As in many handwritten fonts, the strokes in the lambda in VAG Handwritten are rather curvy, but otherwise it’s essentially the same as in most formal fonts, with two sloping strokes meeting at or near the x-height. The lambdas in the OP’s examples are distinctively different, looking like a horizontally flipped L whose baseline stroke curls back on itself. In addition to the η looking like an en (or, as the OP said, like a Cyrillic и) with a tail, the word “κυβέρνηση” has an unusually curly ρ.
The bottom line is that I wouldn’t know how to begin to track down such a font. As far as I’m aware, the online tools that work so well for identifying fonts using Latin characters aren’t designed to work with other scripts.
Find My Font (http://www.findmyfont.com/) has option to search for individual characters (shapes if you wish). It is relatively slow because it has to read all glyphs in each font. There is a limit (programming bug I feel) as it cannot process more than 1,000,000 fonts…
I could give it a try but I don’t know the Greek alphabet enough to recognize matches … or misses or even if it’s doing the job…
As few as that, huh? 
I gave up my search too soon. The replies inspired me to carry on. The result came from searching for “ελληνική γραμματοσειρά χειρόγραφη” and “Images” instead of “All”.
The result was CF Majestic from the Stella project. Similar fonts were Astir and Reclama. The double λλ is an Opentype feature.
Very clever! Your search hint led me to fonts.gr, where there seem to be several ‘CF’ fonts.