Beafer - I wouldn't read anything too devious into the company structure. Each of the three airports is a separate company in its own right. After the deal with Vantage, all three were owned by a holding company called Vantage Airports Ltd, which was in turn owned 65% by Vantage and 35% by Peel. Back in 2012 Peel bought Vantage Airports Ltd's shares in DTV and Doncaster, giving them 100% ownership of those two airports. Earlier this year, Peel bought out Vantage's 65% stake in Vantage Airports Ltd, giving Peel 100% ownership of Liverpool.
So now each airport is a separate company, wholly owned by Peel.
Regarding Liverpool's financial health, I believe it is profitable at the operating level, but that its large debts lead to overall losses. There was a breach of the debt covenants earlier this year, which ultimately led to Peel taking overall control. Presumably Peel's deep pockets have resolved the debt crisis.