Thank you very much, Alan, Sophie!
Midcentury production seems very likely, then...
Wouldn't the fact that the same canes are found in many AVeM "Tutti Frutti" pieces, be a strong hint towards AVeM as maker?
Here is a vase with the "red cross centre surrounded by 4 dots cane": http://antiquehelper.rfcsystems.com/Full/210/68210_view2_02.jpg
Here a vase with the "5 multicolour dots in orange circle cane": http://antiquehelper.rfcsystems.com/Full/059/68059_view2_02.jpg