Think I've got a winner cleaning method for badly coked-up bad-tasting atomizers:
Based on kinabaloo's suggestion of hydrogen peroxide,
and on ted26's suggestion of 'burning it off'.
IN = black really carbon-residue gunked-up atomizer coil & wick.
High street items:
9% (30 vol) hydrogen peroxide (over the pharmacy counter from Boots, 90p for 200ml)
- normally used as a skin disinfectant & mouthwash.
Charged e-cig battery,
or better, switchable 3, 4.5, 5, 6, 9, 12V generic DC power supply (from Argos, £10),
(gives 1.2 amp current-limited at 4.5v, just right

)
Simple procedure:
Wash out atomizer with water, blow out excess water, dry excess
Drip a drop or two of hydrogen peroxide onto the coil with a plastic pipette or whatever.
Connect to power
(i.e. above power supply - which nicely contacts the battery connection-end of the atomizer)
or attach battery & cause it to activate - vacuum cleaner ?, don't suck on it!
Fizzzzz, bubble, & nice steady cherry-red coil for a few seconds.
Maybe repeat once or twice.
Wash with water & dry (I use fan heater about 15 mins, but not so long as to make the wick bone-dry)
OUT = clean white wick (all the way
through), & bright clean coil wire.
Will attempt to get some piccies when I've re-gunked a coil again ...