Northern Rock did not run out of money, it simply lost the ability to borrow money in the credit markets to lend to people for a small turn. The old banking model was very simple, people deposited money and received x% interest and the bank lent the money to someone for x+y%; and everyone was happy. The model of the new era was always based on wafer thin margins and the availability of these funds in the markets.
It is not the losses that have pushed the likes of Northern Rock and Bear Sterns over the edge, but the fact that they had cashflow problems because the asset base(s) was no longer large enough o support the borrowings. Many of the funds out there have borrowings of $30 backed by only $1 of assets, that is all well and good for as long as the underlying assets rise in price, when they do not, they implode.
A 20% fall in house prices will only bring pain to the banks that handed out 90-100% mortgages or mortgages to those who cannot meet the monthly payments (hence the term subprime). The banks that you have mentioned tended to do these through their subsidiaries (by the way, most of these were independent lenders during the last housing boom but ran into trouble and got gobbled up by the bigger lenders), and it will be quite easy for them to let them go bust if they are threatened financially. Northern Rock took all these players on without the financial muscle or the proper corporate structures in place.
Any of them could still go under but it will not be of their own making but rather through contagion.