Buying upgrades with Singapore Airlines

[bizflyer]

Anyone out there know if this is possible after a firm economy booking has been made?

I'm booked out of London with Singapore Airlines to Sydney currently in Economy but might like to upgrade to Business, I've joined Krisflyer but at the moment have zero miles/points etc (this will be my first flight with them).

I guess if they have room in business they would sell me an upgrade, but what might the cost be if I did it, say at the airport on the day of travel?

Thanks