Before you go getting the wrong idea. Do some research, by contacting the manufacturer of the boiler.
Although quite a few manufacturers (Baxi, Ideal for example) will not allow white flue pipe externally. There are also manufacturers that do allow the white flue pipe to run externally. For example Worcester Bosch and more importantly Vaillant (your boiler). Vaillant even recommend extending the white flue externally to maintain any required clearances. They do recommend sealing the external flue clamps with weather proof silicone.
The Vertical flue terminal can also be used like it is in your installation, (even without a lead roof slate) as long as the terminal has the correct clearances around it. Which yours does not!
I've been gas registered for nearly 30 years, and spoke to a friend of mine who is a Vaillant engineer. The advise above, is what their technical department have said regarding your type of flue installation.
What I said in an earlier post still stands. Get a registered engineer out to get it sorted, although you are now armed with a bit more info.
Edit, it would appear that now (from 1st Sept) Baxi allow the white flue to run externally, but only using set dimensions from them, also external joints sealed with silicone.