I don't read the Guardian a great deal, but I'd agree with your obervation.
Bear in mind that their sister sunday paper (Observer) did run an outrageous pro-war fabrication of an editorial long before the war began, and that of course was
before the BBC 'flap'.
That editorial actually resulted in substantial protests in UK activist groups, with many initiating boycotts, etc. I myself was involved in setting up some of those, and wrote a long rebuttal of the Observer lies, distributed in the same circles. Of course, that had no effect, as should be expected.
In any case, The Guardian has often taken an editorial position so extreme it is even contradicted by the Israeli government itself. They even had to publish a correction once (prompted by letters, protest etc - a sanitised letter of mine was printed - can direct you to that if you like).
Also, speaking of the BBC, the head of programming independently circulated private advice (which leaked) stating (this is from memory), that:
"On call-in shows and interactive programming, we seem to be attracting a large amount of the anti-american, anti-Israel crowd. All department heads should be aware of this and try to counter it with balanced coverage."
At the time, public opposition to the plans of London and Washington was about 75%. This shows quite passionate hatred for democracy, again, as should be expected.
The above has nothing to do with the flap, because that happened after this advice was distributed. The flap was largely inane in any case, and the 'judicial' outcome was even more outrageous, at least to anybody with a memory of free speech and democracy.