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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In the United Kingdom it is illegal for any person to manufacture spirits by any means, unless they hold an excise licence for that purpose. If found guilty one could face a penalty of ú1,000 and have their spirit making equipment confiscated. However home brewing of any quantity and strength of beer or wine is legal for ones own domestic use or for consumption by farm labourers employed by said person in the course of their employment.