Free upgrades are very rare unless they are oversold in a cabin, in which case you may do well if you have status with them.
Passengers with status may use miles to upgrade. Skywards Blue can use miles up to 6 hours before checkin, Silver and Gold up to checkin or on board.
Depending upon the cabin crew, you may be able to do a paid upgrade on board. Not sure on the exact price, but I would suspect that you would be looking at £400+ for the MAN - DXB sector.