It seems the best chances for cheap tickets are mid-week and early or late hours - Fridays to Mondays being much more busy I think.

On eurostar at times first class is not much more than 2nd class - due to the fare structure - if cheaper 2nd class tickets are sold out discounted first class ones may not be much more than the best 2nd class fare available and in fist class you do get much bigger seats and a complimentary full meal with unlimited wine, Champagne, etc the whole way!