There are several options ask your travel agent if its an option; the cruise line might do it at no cost as they try to fill up the ship before the sailing date but unlikely you will hear about this until you arrive at the ship. The other way is not everyone turns up last minute cancellations mean higher graded cabins could be available at a price though. I know ships all have signs saying fully booked up etc but see the purser after first day at sea and you might be lucky. We were coming back from Zeebruger on a ferry the worst scenario and having helped others when cruising did the same and ended up in a lovely suite for certainly another £150 but it was a fantasic cabin. Good luck !!
It is certainly not wise on Fred. Olsen Cruise Lines to ask for an upgrade too early or you could be charged the full cost. You may be offered a complimentary upgrade at any time after booking or, as Mr. Blythe says, you can inquire at reception on boarding. Much depends on the type of cruise. On long cruises eg world cruises the ships are heavily booked whereas at less popular times eg early December, the chance of an upgrade is much better.
We are on the Boudicca 3 night cruise in October. I had a call from my agent about 2 weeks ago asking if I was interested in an upgrade from the Balcony Suite we had booked to a Marquee Suite - going up 2 grades - for the price of £39 per person. I agreed immediately and am now looking forward to the extra space. We booked this cruise probably back in May, so not that far ahead. I had not enquired about an upgrade.