Simon Withers, star answerer, sends this definitive answer (10.04):

It's not just London, but a global phenomenon. This excellent explanation,
oddly enough, I found on the Gillette City Wyoming web site FAQ:

'When I put ice cubes that I've made in my freezer into a glass of
water, white stuff appears in the glass as the ice cubes melt. What is the white
stuff and where does it come from?'

A: Ice cubes freeze from the outside, so the center of the cube is the last
to freeze. Ice is pure water, so as the ice cube freezes, all of the
minerals, like the hardness minerals, are pushed to the center. Near the end
of the freezing, there isn't much water left in the center of the cube, so
these minerals become very concentrated, and they form the 'white
stuff' -

the technical name is precipitate. The hardness minerals that cause the
white stuff are nontoxic. If you have a water softener on the cold water
supply you will also see salt deposits from the soft water on your ice
cubes. For best results, a water softener should be connected to the hot
water supply only.

And here's how commercial manufacturers can get around it

(http://home.howstuffworks.com/question205.htm)

'A technique used in most ice manufacturing plants that make large
blocks of ice is to put a tube in the center of the container of water that is to be
frozen. Through the tube they bubble a very low pressure stream of air.
Before the tube becomes ice-bound, they remove it, and they pour or suction
the water that is left in the center of the ice block away. All of the
impurities -- dirt, dissolved air and minerals -- are forced into this water
by the crystallizing ice. They fill the void with fresh water (or not) and
continue freezing.'

--

Charlotte (6.03) Ice cubes
Damn damn damn I read about this in a copy of Martha Stewart Living about a
year ago.One of the readers had written in asking how she could "make ice
cubes like those you get in a restaurant. You know, clear ones." Martha
explained it all. Sorry I can't be more helpful.