I might have all of this completely wrong, so I am sorry if that is the case. As far as I know, you can apply for British citizenship if you have a British grandparent. Is the same true for the Netherlands? My grandfather was born in the Netherlands, then moved to South Africa. Do I qualify for a Dutch passport?
According to Dutch nationality law you can qualify for Dutch citizenship via your parents if they were Dutch at the time of your birth. The nationality of your grandparents is not relevant.
So if neither of your parents were Dutch citizens at the time of your birth, then you do not qualify for nationality via descent.
Also, Dutch nationality law is very strict on dual nationality, and it is only allowed under some circumstances, and in some cases is automatically lost if the person acquires citizenship of a foreign country, or if a dual national at birth and lives outside of the Netherlands in adulthood.
You need to look into it given your exact circumstances. There are plenty of other posts on here about if you qualify via your parents.
BTW: Your statement about British nationality via your Grandparents is also not correct.