How did foolhardy lending to un-creditworthy Americans cause a run on a British bank ......?

and why were stock markets so unnerved?

Ironically, after Bush enacted tough bankrupcy laws on consumers, at the same time he did nothing about the vicious anti-consumer lending practices of the banks. The banks lent out a slew of money all at the same time which in turn caused demand for housing and a huge spike in housing prices, creating a bubble in the housing markets ... during this time, the tax assesors from many municipalites assesed tax rates for homes at these inflated prices, most of which since that time have come down dramatically in price.

As I understand it - the interest is so high (because they are a risk), that in good economic times the people that repay make big profits for the banks, but when the economy gets tougher more people default and the banks loose money. These loans are sold in UK too but we have not had many recent problems with defaults (as yet).
The run on the bank would seem to have been older people who have longer memories and have seen others loose money in pensions and other so called secure places to keep your security for your old age. Lack of trust and a bit of media hype.

Take a look at this article on Bear Stearns, and it will give you a glimpse of the foundation. (Interestingly, it wasn't so much "foolhardy lending to un-creditworthy Americans", but some greedy opportunists at Bear Stearns that cooked some numbers, building a house of cards that sucked in a lot of other big name financial companies). A bunch of stupid saps didn't create the financial crisis reverberating around the world, it was a bunch of brightbulbs at hedge funds that leveraged values way beyond reality.

(Ironically, I did something like this myself in an economics class project many years ago, and so the project was scrapped because the prof thought it "immoral", though legal under his assignment rules. Like with Bear Stearns, I had several classmates investing in my 'leveraged fund' so if I had failed, about half the class would have flunked the project--even though I had taken my own money out already)

That's a long topic, so this explanation is simplified.

A few years ago, when interest rates were extremely low in the US, mortgage lenders reduced their loan standards to generate more business and more profits. This included offering "gimmick" mortgages that had interest-only payments, teaser rates that rose rapidly, and didn't require proof of income. Many homeowners foolishly signed up for these without understanding the terms or without considering what would happen when interest rates started going up and home values stopped rising at high rates.

These mortgages were combined into securities and sold as investments to banks and investment firms, including some in other countries. Earlier in 2007, an increasing number of homeowners began defaulting on their mortgages. Their payments rose dramatically as interest rates rose. Many people were unable to convert their loans to fixed-rate mortgages due to insufficient equity in their homes and high pre-payment penalties.

That drove down the value of the securities that had been sold to the banks and investment companies. As they began writing down these securities, their earnings collapsed and some needed new equity to be invested to keep them afloat. In serious cases, that caused nervousness about whether banks would survive. Consequently, at least one British bank experienced a run on their deposits

The stock markets went down for two reasons. One was that bank and investment company stocks were sold as these companies announced huge losses due to write-downs on the mortgage-backed securities that they had bought. The second was because of fears about consumer spending. Consumer spending impacts corporate profits and, consequently, stock prices. That's especially true in the US where savings are very low and consumers commonly finance their lifestyles by going into debt. People who can't pay their mortgages don't buy cars, go on vacation, or otherwise spend lots of money. Investors feared that corporate profits would be impacted and so they sold stocks.

Many banks (including UK and Euro banks) owned large quantities of mortgage backed CDOs that went bad and collapsed in value.

Why/How did the CDO's go bad? The Wall Street Journal had a decent front page story today on how a particularly nasty CDO called "Norma" went bad.

These CDO's combined rather low grade mortgage backed securities together to yield some CDO's that got a Fitch AAA rating.

How the heck do you get a AAA rating on low grade stuff?? The securities were combined via derivatives that coupled together securities with supposedly uncorrelated risks or anti-correlated risks. Does anyone remember Long Term Capital Management?

The problem with the fancy math of uncorrelated and anti-correlated relationships is that it always depends on a stable environment experiencing small perturbations. Does anyone think that the sub-prime/alt-A/maybe-prime mortgage meltdown is in anyway stable or small?

The end result for Norma, was a CDO that was rated AAA one month and then rated junk a few months later. Fitch's excuse was that the world had changed in those few months, & their ratings reflected that. What a load of crap!

GREED!!!