From your Blix link:
"The war was not legal even if Iraq has breached several of United Nations resolutions, said Blix to the British paper The Independent."

The foundation of the legal argument isn't the UN resolutions- except in the sense that the cease fire agreement was incorporated into a UN resolution.

"I don't buy the argument the war was legalised by the Iraqi violation of earlier resolutions, Blix said to the paper."

Again, it wasn't based on a violation of a UN resolutions, but rather a violation of a cease fire agreement. This was strengthen by involving the UN, but by itself the violation of a cease fire agreement was sufficent grounds. [Though the UN did confirm that Saddam was actually violating this agreement].

"According to Blix, it would have required a second United Nations resolution explicitly authorising the use of force for the invasion of Iraq to have been legal. "

This wasn't a legal requirement. If you were in a similar situation without a cease fire agreement, and the whole UN security Council and even a huge majority of the rest of the UN general assemble, had authorized the use of force- to remove Saddam's WMD [or some other country's WMD], it would similar to a lower judge making a bad decision (it wouldn't be in accordance to international law [in other words, by making a judgement it would in affect be making a law, but then this would have introduced "unresolvable" conflicts within international law).
The only legal reason the UN was in Iraq removing Saddam's WMD was because Saddam had agreed as a condition of ending the war that he would rid his country of WMD. If say, instead, the agreement was promising to plant a 1000 palm trees- and if Saddam had failed to fullfill that, he would also be violating the cease fire agreement. Though by putting "planting a 1000 palm tree" in the agreement would been rather stupid- because there would be little political will to enforce this agreement. Whereas there is a fair amount of political will to see the curbing of WMD around the world- therefore it's more "enforceable" and therefore somewhat reasonable to put in the document as a condition of stopping the war.

Btw, the UN did pass a resolution regarding Gulf war I- it said Saddam's invasion of Kuwait was illegal. But again, this resolution wasn't neccesary- Saddam had violated international law, and without any UN resolution, the US (other any country) could have legally started war with Saddam's regime. But it was helpful for the UN to pass this resolution, and also gave Saddam an opportuny of withdrawing from Kuwait without meeting the full wrath of international community.

So, Blix is clueless. And since he was a UN inspector this is somewhat disappointing- but the good news is, being a legal expert was not really his job.