How can I find out if a particular cruise is filled up? This would mean that upgrades would be unlikely, doesn;t it?

If a ship is not filled up you will see some last minute price drops. Since cruise ships are sailing now at almost full capacity I think the chances of upgrades are slim. If you do get an upgrade it's more likely to be cabin location upgrades, not full category upgrades, at least from what I've been reading recently.

On certain companies ( P & O being one of them) you can try to book online, they will then show which cabins are available.

Travelocity has a good site for checking cabin availability. Go into the cruise you're curious about as though you're going to book it. Choose the lowest category offered, then one category at a time, keep upgrading your self. You can see (up to 7) how many cabins remain available in each category, although some will show just a guarantee. I did this recently for our April cruise on the Dawn Princess. At that time they were showing 91 cabins (including guarantees) still open for our sailing.

By the way, this will be our 15th cruise in just over 7 years. We've NEVER been upgraded!