emorge
Some tickets are not upgradeable, and with others it can be very expensive, it depends which class of ticket you hold in the first place.

At LHR I have seen someone ask at the last chance desk about an upgrade, only to be told a large fee and payable only in cash.

At BKK whilst on the aircraft 2 Elite class passengers asked the fare to upgrade, they decided to stop where they were, so do not expect any bargains I am afraid.