As far as I'm aware, there are no laws against distilling your own spirits. It's the same as brewing your own beer, or making your own wine. The laws only come into effect if you start selling it for a profit. Even then, I doubt the local bobbies will roll if you put half a dozen bottles of your Dandylion & Burdock up for sale at your local Bring&Buy.
As for the taste, it depends what you start with, but commercial Brandy is distilled wine, so that gives an idea of the possibilities.
Vermouth is a "fortified wine"--like Port, Sherry Maderia and Masala--which is just wine with the addition of a small percentage of spirit (often Brandy) to preserve it.
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