"It can't be tax avoidance if no tax was avoided."

Ha!

From the BBC:

Mr Miliband has confirmed his mother Marion set up a deed of variation after the death of his father Ralph... the deed allowed ownership of the house to be split between Mrs Miliband and her sons [rather than going to Mrs M outright]. The paper quoted experts suggesting such arrangements could be used to reduce tax liabilities.

Mr Miliband later sold his share to brother David who also bought the rest of the property from his mother. But a Labour spokesman said: "Ed paid 40% capital gains tax when the house was sold in 2004/05. It can't be tax avoidance if no tax was avoided."

This is taxation for idiots. The rate is one thing, the tax base is another.

Inheritance Tax and Capital Gains Tax (at the time) were both 40%.

The difference is that Inheritance Tax is payable on the full value you inherit and CGT is only payable on the increase in value between when you inherit it and when you sell it.

So, by a circuitous route*, the sons ended up saving IHT of 40% x whatever the IHT nil rate band was at the time (£200,000, probably) when Mrs M died.

For Dave, who moved into the house, that was an absolute saving (future capital gains are exempt).

For Ed, the increase in value between when he inherited and when he sold to Dave was taxable at 40%. So he paid 40% on some of his ultimate proceeds but not on all of it, which he would have done without the deed of variation (40% IHT on value at date of death and 40% on future increase in value).
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* The circuitous route...

The original deed did not reduce the IHT bill on Ralph's death but was (almost certainly) done in order to use up his nil rate band. Most transfers to widow or widower are exempt anyway, but his sons inherited a share of the house worth as much as the nil rate band was at the time, with no IHT. This is then their base cost to deduct from a future sale to calculate the capital gain (if any).

So when Mrs M shuffled off, the value of her estate was correspondingly lower and so the amount of IHT which the sons had to pay when they inherited from her was less than it would have been without the deed of variation.

While this is bog standard IHT planning, the whole thing is now redundant because if the deceased did not use up his/her IHT nil rate band with transfers to other relatives, the unused bit goes to the surviving spouse, so it can be used when he/she dies.