If they are tax resident in Spain, which it sounds like they are, then I imagine they will have to pay IHT in Spain, deducting tax paid in the UK under the terms of the double-taxation treaty.
In the UK the estate of the deceased pays the IHT, in Spain it’s the beneficiary of the estate. UK IHT of 40% above personal allowances (currently £325,000 per person) is higher than Spain, if I’m not mistaken.
You’ll have to check with a tax expert but my guess is the estate will pay all the IHT in the UK, and thanks to the double-tax treaty there won’t be any more to pay in Spain (just lots of paperwork and legal costs). Shame the estate is not in Spain because in that case your parents would pay less IHT.
I’m not expert in IHT. You’ll have to check all this with a qualified solicitor with expertise in both jurisdictions.