For someone who is generally cynical about this government, Phil, you seem surprisingly keen to accept their statistics in this area.
The way I see it, the "official" figures on benefit fraud are produced by civil servants who work in the DWP and other departments responsible for paying benefits. So they have a huge self interest in not looking too hard into fraud, because large numbers will inevitably make them look bad. Obviously their goal is to come up with numbers which are large enough to be plausible, but small enough to be tolerable. And judging by the number of people who say that benefit fraud shouldn't be a priority compared with, say, tax evasion, they've judged it about right.
But what is the true level? I don't know, you don't know, nobody know.
This website makes a good argument that the total is £5 billion or more, rather than the £1.2 billion official figure. I don't know who's behind that website or what their agenda is, so I should stress that I'm disinclined to trust it too far. But they point out that many indirect ways of estimating benefit fraud (e.g. the test study which showed that a large number of people would rather sign off jobseeker's allowance than turn up for unpaid work) come up with significantly higher estimates.