Jack Hawkins did not receive an Oscar nomination for portraying Major Warden in The Bridge on the River Kwai.
Hawkins differs his performance nicely from Guinness's and Hayakawa's work by playing Major Warden as perhaps just a little bit more self aware than the other two. Hawkins brings a bit more of a purposeful humor to his performance, although Guinness does that to although he shows it as an accidental element of just how proper Nicholson does. Warden instead brings just a bit of playfulness almost in how he handles the stiff upper lipped manner of Warden, as though Warden is certainly in on his personal style to a certain degree. He's particularly good at this in the scene where he asks Holden character's about going on a mission to destroy the titular bridge. Hawkins plays the scene as though Warden is playing with Shears the whole time as he portrays the refined concern as Shears reveals he lied about his rank, but then this works perfectly as Hawkins suggests a purposeful joke, for Warden's own amusement only, as he keeps the same reserve as he reveals that Warden has been aware of this the whole time intending to use it basically even as blackmail to ensure Shears's participation in the job.
The madness still is quite evident in Warden though as Hawkins brings such a callousness in the way Warden seems to treat all things. Even though Hawkins makes more amiable than Saito and Nicholson, the way he play with lives is still there. Hawkins actually makes the humor of Warden rather dark in nature, because he keeps his humorous British reserve no matter what he is talking about early on. Whether he is talking about plastic explosives, knifing a man, or potentially getting killed in a parachute run Hawkins is effective by showing the madness in the way Warden treats all of his in such a lighthearted way. Now Hawkins is good in again he differs somewhat from the other mad men, but somewhat suggesting that maybe Warden isn't quite as fervent as others in his views. Hawkins mostly alludes this subtly through his reactions suggesting the awareness in Warden, and this slight fault in the armor is important once Warden goes on with the mission and leads them to destroy the titular bridge.
Once on the mission Hawkins drops all the humor suggesting that Warden does take the mission very seriously. Hawkins does not drop the sense that Warden does still have that madness as he even views the death of one of the men simply a set back in his game. This cracks suddenly though when Warden is injured and this may not have worked but Hawkins's reaction is perfection. His reaction is both a shattering of his facade of his ease, but also almost a moment clarity as he seems to understand where he has gone wrong. For the rest of the film Hawkins plays the injured Warden as an understandably far more sorrowful yet more empathetic man. It's technically a sudden change of heart but one that Warden succeeds by suggesting some doubt in the man before as well as delivering in the pivotal moment. Just like almost everyone else in the film Hawkins is great in the final scene with every powerful reaction as he shows Warden finally feeling the weight of his "game" full force without his sort of madness to blind him. I won't say Warden reaches the great heights of Hayakawa and Guinness, he still succeeds in giving a rather fascinating portrait of a well refined mad man.