Think you can usually book it on board but you won't get a bargain.
We are on Celebration end July for 2 weeks and, like Colin, booked a year in advance so got AI included.
We have always done Thomsons, and keep on thinking we will try another cruise line (we will one day!) but end up back with them again - for example this year we wanted a different itinerary than the Western med, which we have done many times. For us Thomsons offered the best itinerary round the greek islands and adriatic - the choice didn't seem huge as a lot of cruise lines seem to sail out of Southampton, which we didn't want to do or didn't seem to offer 14 night cruises.
As I say - one day we will try another line, but have always thoroughly enjoyed our Thomsons cruises - especially with AI included!!
Gill