In a strictly hypothetical situation where I had a reasonable sum of money in savings in the UK (my country of origin), and I had moved to the Netherlands, would the Dutch government require me to declare and then tax me on those savings?
Not if you have 30% ruling.
30% Ruling and Box 3 of your tax return
Under the 30% ruling you can opt for ‘partial non-residency status’. You are then considered to be a non-resident tax payer in Box 2 and Box 3, even though you are living in the Netherlands. For Box 1 income you are considered a resident tax payer, therefore you do not pay income tax on assets in Boxes 2 and 3 (except for real estate located in the Netherlands and substantial shareholding in a Dutch resident BV) and you are entitled to the partnership ruling in Box 1.
Bank savings and 30% ruling. Foreign bank accounts. What to declare?
Benefit of the 30% ruling is that in the annual income tax return you can opt to be treated as partial non-resident for tax purposes. This means that you can declare your income as if you are a non resident but on the other hand still claim tax deductions as if you are resident. Benefit of this option is that you will not have to declare all your savings and investments in Box 3. Bank savings for example will not have to be declared in your Dutch tax return. The "assumption" is that you will declare these in another country but this will not be checked and is not a requirement at all. [...]
Summary: In general, the Dutch tax office cares about your worldwide income and assets and you can be taxed on savings abroad but you might also be eligible for a rebate or even omit some of your assets and income entirely depending on your situation.
You generally have to pay income and capital/wealth tax on your worldwide income and assets, not only on your Dutch savings. See in particular Income abroad on the Dutch tax office's website. Particularly relevant here is that the Dutch income tax includes a sort of wealth tax because savings are assumed to provide a 4% interest rate (forfaitair rendement) and you have to pay a 30% tax on this fictive income, no matter how good or bad your savings really did in a given year (it's called “box 3 inkomsten” in Dutch tax parlance).
The details of how much you have to pay will depend on tax treaties, EU rules, and possibly the “30% ruling” but you might at least need to declare those savings and you are yourself responsible for doing it correctly.
Normally when someone immigrates to the Netherlands, this person is taxed there on his worldwide income. The Netherlands also taxes its residents on their deemed income from their worldwide savings and investments. The tax is 30% of a 4% deemed return on their investment (so 1.2% on their net wealth).
If this person would hold the 30% ruling, this may all not apply to this person. He can opt to be treated as a foreign tax payer for his income on savings and investments. This way, only Dutch real estate is taxed. No bank accounts or investments at all have to be declared in the tax return.Read here if you want to learn more about the Dutch 30% ruling.