Wrt the airport vs airline responsibility question, in the UK, there is no problem issuing a single summons against both. Then assuming the judge decides in your favour, he/she will also decide who coughs up, and by how much.
There is greater incentive for either of them to agree a settlement out of court, in order to avoid the potential situation of their expensive lawyers attacking/defending each other for an extended period, rather than just trying to demolish your argument.