I think we need to get a bit more radical to solve what is a generational fairness crisis.It depends whether you think people should have the right to pass on their wealth to their descendants. A certain amount of inheritance tax is reasonable, but as I do think that people should have the right to pass on their wealth as they see fit I certainly wouldn't go as far as your first sentence.
We're heading to a position where a large proportion will receive many hundreds of thousands of £ (1 in 5 retired households being millionaires), where others will simply never be able to even buy a home. None of which is reflective of their own efforts.
My preference would be something like a 90% IHT rate, after relevant costs of death and probate, and then give all people at 18 a £25,000 bond which can be cashed in for certain purchases (house, qualifications, business startup etc), or otherwise just money in their pocket at a later age cutoff.
Current IHT raises £5billion+ per year, so it's easily affordable on a 90%IHT.
It's clearly not a grey-vote winner, but I see only benefits to society.