Yeah, I concur that it's on the value of the estate of the person who died.
But there is also this: "The standard Inheritance Tax rate is 40%. It’s only charged on the part of your estate that’s above the threshold."
And given the threshold rises to £500k when it's between direct family (parent to child, etc), and you're only paying on the value above the threshold... you have to inherit a pretty big house from your parents to even have to pay inheritance tax. Say it was a £550k house, so there's tax to pay on the £50k over half a million. 40% of that comes out to £20k, which sure, is a lot of money... but getting a little £20k mortgage on that massive £550k house you just inherited would absolutely be viable. I think the overlap of people with family wealthy enough to have £500k+ houses, but who themselves are so low paid and have such a low credit score that a tiny mortgage is literally impossible, is really, really low. Like there could be a few edge cases, but I'd be willing to bet the majority of people who are in a position to inherit a £550k house are also in a position where a £20k mortgage would not be hard to arrange, especially given they now have a high value asset to secure the mortgage against.