if the loan is taken out in the operating business name of Newcastle airport then the airport is responsible for it like any other business would be regardless of ownership.
However the business can pay out of funds it has or ask its shareholders to inject more money (as has happened in a lot of businesses recently) or one shareholder could inject more money and increase their stake at the expense of the other or one/both shareholders could loan the business money to pay off the debt but it would be treated as a loan on their books and interest could be paid on that in the same way as it is to a bank.
It is unlikey that one of the shareholders is responsible for the entire loan unless it was part of some agreement at the time this was undertaken or unless one of the shareholders were underwriters for the loan i.e if Newcastle Airport cant pay, then whoever legally agreed to back it (in order to get the loan in the first place) could be liable.