SOME benefits AREN'T means-tested, so savings are irrelevant.
MOST benefits ARE means-tested. Commonly savings of up to £5000 don't have any effect on those benefits but from £5000 upwards benefits start to be reduced and they disappear altogether once the level of savings reaches £16,000.
However the rules vary between different benefits, so we need to know WHICH benefits you're referring to in order to provide a definitive answer.
The main unmeans tested benefits are
old age pension (!) yup now classed as a benefit - I was "granted it" on application earlier this year and
DLA / now PIP ( personal independance payment ) - and associated attendance allowance