This question is inspired by Hellsing Ultimate. In it, a secret splinter division of the Nazis left at the end of World War 2 remained in the shadows building up power, until the events of the anime where they reveal themselves by flying Zeppelins into London and razing it to the ground. Oh and there are vampires too! Let's ignore that last point however.
This made me wonder...
Take a world that is identical, up to now, in every way to our own. Unknown to us, a secret organisation (To reduce the chance of offence to readers of this question, these are not Nazis). The various world governments have no intelligence on this organization - not even that it even exists. Nor do they have any reason to be suspicious. Suddenly, and without warning, Zeppelins are spotted flying across the English Channel. As they approach London, they start firebombing the city, deploying other advanced weaponry, and then depositing troops to mop up any remaining civilians. Similar events occur at the same moment in time at other major cities all around the world. (Note: How they got this far without being noticed is beyond the point of this question)
The opposing force has had a long time to plot this attack, and place resources in places that make it possible. They have either managed to get spies/sympathisers into the various world governments, or the military bases of these governments were earmarked as priority targets in the first wave of attacks.
What would happen next? I am mainly interested in military responses from the countries affected, but other forms of response from civilians is acceptable.
This should as realistic as possible. However, one condition any form of surrender by the opposing force is not an option, because like the anime that inspired this question, the commanding officer's does not simply like war, but loves war.
(Sorry if this question is not appropriate for the World Building site. It is my first question here, and I'm worried this falls under the 'open-ended question' rule.)
You can probably tell that I didn't really think this question through properly when I asked it. I have accepted fgysin's answer, but credit to o.m. who backed his answer up with some impressive statistics. Please consider this question closed.