To be '''Nibbled To Death''' means that you've been charged for this, charged for that, charged for every little thing, and while each charge on its own may have been insignificant, the totality is overwhelming.

Banks in the UK excel at this.

The phrase often heard in the U.S. is actually "Nibbled to Death by Ducks" ... Same phrase?

I believe here in the UK it's more recognisable as what happens to students. ;-)

''Actually, in The Good Ol' US of A we say, "Nickel and dimed to death," meaning small charges applied all over the place that add up to a large drain on finances.'' - Indeed, if you click on the title of this page you'll find it referenced by NickelAndDime.

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                Charge'em for the lice
                Extra for the mice
                Two percent for looking in the
                mirror twice.
                Here a little slice
                There a little cut
                Three percent for sleeping with
                the window shut.
                When it comes to fixing prices
                There are lots of tricks he knows
                How it all increases
                All those bits and pieces -
                Jesus! It's amazing how it grows.

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''Google sez:''
* "nickeled and dimed" - about 2,460
* "nickel and dimed" - about 41,200
* "nibbled to death" - about 5,950
* "nibbled to death by ducks" - about 807 - now it is 167,000 
* "nibbled to death by cats" - about 2,920
* "nickled to death" - about 3, pun seems to be intentional
* "death by a thousand cuts" - 217,000

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A particular form of "death by a thousand cuts".

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See: AmericanCulturalAssumption, BritishCulturalAssumption