Ah, close, sounds a lot more screechy with a higher note at the end.
We get a lot of Greenfinches here also, so I wouldn't be surprised if it was, but not this time.
Just listening to this, not even close :(
www.youtube.com/watch
I'd say that is either a Robin or more probably a Blackbird. They both make that 'mewling' noise, but in my experience, the Robin makes a slightly longer sound than the Blackbird.
Unicum arbustum haud alit duos erithacos
(One bush does not shelter two Robins)
Zenodotus (3rd Century B.C.)