The argument is over the following:
Vodafone (company D) has a subsidiary (subsidiary D) which in turn has a subsidiary (subsidiary DD). Both subsidiaries are based outside of the UK. Subsidiary DD pays billions of Euros in interest payments to subsidiary D as one of the outcomes of the acquisition of subsidiary DD. HMRC believed that subsidiary D's profits can be taxed in the UK. Vodafone disagreed:
In a nutshell, Vodafone's argument is that EU rules override UK law in this instance.
Despite having a decision in their favour on the application of the controlled foreign companies (CFC) laws overturned in the Court of Appeal, Vodafone still had two defences - first, the "motive" test, i.e. that there is genuine economic activity going on in the subsidiary rather than it existing only as an artificial arrangement for tax avoidance, and second, that this case doesn't fall under the limited circumstances when the CFC laws can be applied as set out by the ECJ in the judgement of the Cadbury Schweppes case.
Rather than take it to litigation, an attempt was made to settle the case which ended up with Vodafone paying over £1B to HMRC. Sir Andrew Park said of the settlement:
So settlement was the pragmatic option given that zero tax would be due in the likely event of Vodafone winning the case. Not only that:
So if Vodafone had litigated and won, it could have set a precedent meaning that the companies involved with the other disputes could also have won and therefore would lose HMRC large amounts of tax revenue. Sir Andrew Park also said:
...the settlement reached was a good one and represented fair value for the wider taxpaying community.
It is also worth mentioning that the case had been running for the best part of a decade before it was settled.
As for the £6B figure that Vodafone was "let off", that number comes from Private Eye magazine and there is nothing to support it.