His evidence for this is pretty weak. Essentially, he has two points. First, that by publishing the story on their website before the interview they pre-empted his interview and thereby prevented people getting the balanced and nuanced account of his opinions that the interview provided. Second, that the website article was distorting.
I don't know Wardman's background. If he hasn't worked in journalism or politics his mistake in assuming that an article published before the actual interview runs is exceptional is quite understandable. It is quite common to trail an interview a little. A couple of examples off the top of my head that were definitely trailed by news stories in the media before the actual speech: Patricia Hewitt's speech on the next ten years of the NHS and the Dispatches programme investigating the Olympics. In fact, the process is so common that if I read an account of the contents of a speech in the newspapers I will usually expect that it is still possible to go and see it.
What has happened here isn't so different. The Archbishop made the statements cited in the BBC article in a pre-recorded interview. They will probably have put the website story up first on the assumption that people hearing the interview would go to look it up on the website and, if the story weren't in place, it would leave them dissapointed. That is the same reason TPA research reports generally go online late the night before they hit the papers, shortly after the first editions have hit central London. There's nothing sinister about it - just good planning.
So, is the website article itself misleading? I don't think so. Wardman's main accusation is this one (which he repeats endlessly):
"The story was trailed at the top of the news programme with the headline: The Archbishop of Canterbury has said that the adoption of Sharia Law in some parts of Britain is inevitable. (No he didn’t, or not in the way that your headline was inevitably going to make people think.)"
The Archbishop did say "it seems unavoidable". The website's account of that, crucial, statement isn't in any way misleading. It was followed, very near the top of the article, with: "For example, Muslims could choose to have marital disputes or financial matters dealt with in a Sharia court." I don't see anything that is missed here. I don't see anything misleading in the website's account of the interview at all. Wardman is being completely disingenuous and I get the impression he is only able to convince himself because he is working from the assumption that people must have been misled, must be behaving irrationally.
There is a real arrogance to Wardman's unstated assumption that the public are just useful idiots for the media - charging at a red flag. He doesn't take the time to understand why people are angry. He should.