Wow, that is pretty shocking.
That's not shocking, that's
scary! One third of the population is dependent upon stealing from their neighbors. How does that sound as a recipe for social harmony?
I don't know what data and calculations they used, so what follows is just baseless speculation.
It's possible that 1/3 of the population is dependent on getting money from the rest.
But it could also be possible that a lot of those "dependent" on benfits are only require state assistance as a result of the state taking so much off them in the first place.
Take for example the Tax Credits mentioned in the article. I don't know the exact details of how they work, but basically, rather than the government just reducing taxes, they decided to keep them at a high level, but create a mechanism for (some) people to claim some of their money back.
So while it would be a valid criticism to say this is making people less self-sufficient and more dependent on the government, its not necessarily true that this many people are living at the expense of other people.
As for how much tax we pay:
At the last general election, one of the leaflets I got in the mail from the Liberal Democrats claimed that, after all the various taxes and tax credits are taken into account, the richest fifth of the population pay on average 41.x% of their income in taxes, and the poorest fifth pay 41.y%, where x was slightly smaller than y (I can't remember the exact value). (They didn't say anything about the middle three fifths).
Of course, that was about two years ago, so they may have gone up since then. (And I'm not sure how much I'd trust any statistics used by someone trying to persuade me to vote for them, anyway).