in the end, at who's feet did the blame fall?

Most of the blame ended up falling on Lucan but there was plenty to go around. Raglan, Lucan, Cardigan, and Nolan all made mistakes that ended up building into the charge but Lucan was the one who could have stopped it.

The film sums it up very well in the last minutes: "Him." "Me?" "You." Lucan was recalled and never saw active service again (but was promoted to General and eventually Field-Marshal). Raglan and Lucan slugged it out in 'The Times' for a while, each blaming the other in print.

Cardigan came home a hero but was accused of turning tail immediately after the charge. He sued for libel and lost, and the judge noted he was "absent when his presence was desirable".

Take your pick!

Flashman does not blame Cardigan, though there was no love lost between the two. He attributes the disaster to Raglan and Airey.

Well, Raglan, who gave the order but didn't make it clear what exactly the orders were, or if he did Airey didn't write it down. The order simply said the cavalry were to prevent the enemy carrying away the guns, but didn't specify which guns. This was obvious to the senior officers on the Fedioukine Heights, but not to the cavalry in the valley who couldn't see what was happening. Nolan may have contributed to the disaster by not passing on any verbal instructions he may have been given by Airey, but the ultimate blame must be Raglan's.

Read a book.

Raglan gave the command. Airey wrote it down and read it back to Raglan. Nolan carried the order to Lucan. From that point on, it was the senior command in the field's responsibility to carry out the order. Recall that Raglan said something to the effect that he expected the cavalry to attack the enemy's flank when instead they were charging straight down the middle of the valley. Should Raglan have specified how he wanted the attack carried out or should Lucan or Cardigan have known how to do it is the question. As written, the order was rather vague but as anyone knows who has been in the military, it's always the senior commanding officer who has overall responsibility and therefore shoulders the blame.
KS

I'd say you have to give Raglan the lion's share of the blame. Giving Nolan a vague and contradictory order was the primary problem here. The personal animosity between Cardigan, Lucan and Nolan would not (at least on the basis of evidence presented) have been a problem if Raglan had made himself comprehensible in the first place.

"I shall tread uncommon wary and keep my pepperbox handy."

SPOILER

I liked the ending, somewhat unexpected, yet faithful to the whole picture. Men arguing who's fault was it, then the credits roll, there's no music only the sound of flies buzzing over a dead horse.

I guess all of them were guilty at some point and in some measure. It's war and there's no words for it.