The Royal Bank of Scotland is the key

The development which almost certainly led to the government taking the final decision to launch, literally overnight, on Tuesday its financial rescue package for the banks was fear over the situation with the Royal Bank of Scotland (RBS). RBS is a giant. By assets it is the largest private sector bank in the world - its assets on 31 December last year standing at $3.8 trillion. http://www.bankersalmanac.com/addcon/infobank/wldrank.aspx
RBS therefore entirely dwarfs Northern Rock, Bradford and Bingley, or HBOS - the largest British institutional victims so far of the financial crisis.
The fall in RBS's share price between 2 December 2007 and 8 October was 87 per cent. Such a fall means the market considers that the bank is on the verge of collapse. To give a comparison, shares in HBOS, which had to be rescued, fell by 88 per cent over almost exactly the same period and Bradford and Bingley's shares had actually fallen by less when it was nationalised.
RBS, together with Lloyd's TSB and Barclay's, was one of the banks reported to have approached the government for a capital injection on Monday night. However neither Barclay's nor Lloyds TSB were in the same state of collapse of their share prices as RBS. Almost certainly, therefore, it was fear over a collapse of RBS that led the government to take action at such extreme speed.