Airlines generally will not sponser and pay for your work permit - you need the right before you you apply.
If you are not EEA/EU passport holder, then being the partner or spouse of a settled UK resident is the way to get the leave to remain in the UK.
Some airlines ask for permanent leave to remain which you get 2 years after the initial visa. If they ask for permanent leave to remain/right to live and work in the UK, you cannot apply with temporary "visit UK" work visas such as given to Australians.
EasyJet is one example of an enlightened company that takes on suitable candidates of any nationality as long as they can fly to all their destinations without the need to apply for a visa, and that they have leave to remain (even if only temporary).