Inheritance Tax really only exists to prove some sort of point rather than to raise very much revenue, so abolishing it is actually not such a bad idea. But only as part of wholesale reform of the tax and benefits system, such as could never be proposed by John Redwood, nor ever brought about by any of the existing parties.
All income below national median earnings should be made tax-free, and all income above that taxable at a very low flat rate with no further arrangements, while guaranteeing everyone an income of at least half national median earnings by means of single form of payment called, and effecting, Social Security.
This would cost next to nothing to administer. And there's no point claiming that it would benefit the hugely rich, because, on the contrary, they hardly pay tax at all as things stand. This way, they would.
Likewise, every company should have a corporation tax allowance of half national median earnings multiplied by the total number of its employees, so that it had enough to pay each employee that as the minimum wage, and then be taxed at a flat rate as above, finally getting to the currently tax-free profits of the richest companies.
And that flat rate should be permanently higher (with strict regulation to ensure that no cost was passed on to workers, consumers, communities or the environment) on the banks and on the privatised utilities, recalling a Tory and a Labour windfall tax respectively, and yielding the funds necessary to reimburse employers' National Insurance contributions for workers aged 25 and under, aged 55 and over, or for as long as a previous period of unemployment lasting 18 months or more.
Within this, both Inheritance Tax and Capital Gains Tax could be abolished. But not otherwise.