"I don't think it's banks we owe money to."
It is. In 2009 to 2010 we added nearly another $150 billion to the massive pile of debt, 24% of the money the Government spent. And that money has to come from somewhere, which is banks. Most of those banks are foreign banks, but as you're seeing with the Greek problem all banks are linked. If the British banks collapsed they would collapse owing other banks money, and that chain of owed money would eventually bite us as banks become no longer able to lend us money or push the price of borrowing that money upwards.
Look again at Greece where there is a massive problem making sure that they can borrow the money they need to keep their economy running.
So we are very dependent on the banks. If we couldn't borrow money we would, as said above, be facing 25% cuts in spending or 33% tax rises.
And as if 60 years of Government over spending isn't bad enough this country also engineered an economy that was based heavily upon the financial sector. So if that does collapse not only would our ability to borrow be hit but Government revenues would fall. So we'd need to borrow even more money.
So this country cannot allow the global banking system to fail because it needs that banking system to fund it's public spending and it needs our portion of the global banking system to provide a large chunk of it's income.
If we'd lived within our means and kept a diverse economy then we could afford to give the banks a good kicking. We didn't and therefore we can't.