They are 100% owned by the British government. There’s nothing privatised in the UK and never was. And that’s why they suck so hard.
As for German involvement - the British government just outsourced day to day operations to Germans and others. Just like they outsource No. 10 floor wiping. That doesn’t mean that No. 10 is privatised. It’s the choice of the government and that’s how they decided to spend their budget.