The government sets the priorities of the agency, both major parties love quangos because they can pass the buck, pretending it's nothing to do with them. If the people want traditional flood protection it isn't going to happen, it will take billions that no party is going to spend.
It's all about natural buffering nowadays, Salt Marsh, slow river flow etc. nice, cheap and most years functional.
It's really not an issue I know a great deal about, but from my limited understanding, when the environment agency was created about 20 years ago, they took a slightly more "hands off" approach that would encourage a more natural environment - good for biodiversity, good for natural habitats for animals and all that lark. The problem, though, is that this isn't natural land. 500 years ago or so, it was all marsh land and some Dutch engineers help craft it into useful agricultural land, and since then it has required human "interference", if you like, to ensure it doesn't flood. Obviously this year is particularly bad in terms of the weather, but my understanding is that in an attempt to be more "natural", the environment agency has effectively stopped doing all the things that have been done for centuries, like dredging the rivers to make sure there's enough spare capacity in them to carry away what would be the marshy water through the drainage system without flooding over its banks.
That's just my understanding from reading a few articles from irked Somersetters though, so perhaps they're just looking for scarecrows.
Edit: Further, I see no problem with what Gove did to the Ofsted woman at all. You can call it "politicising" if you like (though they obviously already are - Labour absolutely stuffed the quangos with their people in 97 and it's never swung back the other way; they're still overwhelmingly steared by people who are politicially aligned to Labour by their own estimation) but I don't think there's anything wrong with the elected government of the day putting people into jobs in otherwise unaccountable agencies. That's the only, limited, slither of democracy at play in most of these agencies, and I'm all for it (and I have no problem with labour installing its own people in 97 either, my only problem is that the Tories and Lib Dems didn't do the same in 2010).