Exactly when did Capt.Smith know the Titanic was doomed?

The answer to that question determines how swiftly the Captain reacted to order the evacuation of the ship.

Some commentators have said Capt. Smith didn't know for 45 to 50 minutes.  As I demonstrated here--
http://titanicsecrets.blogspot.com/2009/07/first-boats-cutting-gordian-knot.html-- the Captain knew in less than half that time that the Titanic was sinking and there was nothing he could do about it.

Now I've uncovered a long-lost newspaper account that narrows the time frame more precisely.

Fourth Officer Joseph Boxhall was asked the question specifically at the British Inquiry into the sinking of the Titanic.

May 22, 1912
British Inquiry

15610. Did you hear the Captain say anything to anybody about the ship being doomed?
- The Captain did remark something to me in the earlier part of the evening after the order had been given to clear the boats. I encountered him when reporting something to him, or something, and he was inquiring about the men going on with the work, and I said, "Yes, they are carrying on all right." I said, "Is it really serious?" He said, "Mr. Andrews tells me he gives her from an hour to an hour and a half." That must have been some little time afterwards. Evidently Mr. Andrews had been down.

15611. Can you tell us how long it was after the collision that the Captain said that?
- No, I have not the slightest idea.

15612. Did you say as a matter of fact in America that it was about 20 minutes after the collision?
- No, I do not think so.

15613. You could not fix the time?
- I cannot fix the time; I have tried, but I cannot.

I have discovered the source of that question, and the telling answer that Boxhall failed to give in England.

Exactly one month earlier, on April 22, 1912, Boxhall testified before the U.S. Senate Inquiry into the disaster.  A week after that, Sen. Theodore E. Burton. a member of the panel hearing evidence, had a private meeting with Boxhall. The fruit of that meeting was revealed the next day. Associated Press reported the story and it appeared in newspapers on April 30, 1912. I've found it in the Boston Evening Transcript and the Trenton True American. Here it is as printed in Pittsburgh's Gazette Times, May 2, 1912:

(Associated Press to Gazette Times)

White Star Line Withheld News 12 Hours

Captain Felt Doom

Washington, April 30---Before the hearing was resumed today Senator Burton announced that he had examined Fourth Officer Boxhall late last night and had learned from him that J.W.Andrews, builder of the Titanic, who went down with the ship, told Capt. Smith after the collision that the boat would sink within an hour.
:"I had a long talk with Officer Boxhall," said Senator Burton," and asked him to recall if he could what he heard Capt.Smith say on the deck of the ship after the collision. Boxhall recalled several trivial things that had been said on the bridge and about the deck before the order was given to get out the lifeboats and then recollected what the Captain had said about the condition of the ship a few minutes after the collision.

                 Captain Knew He was Doomed

He said Capt. Smith had told him about 20 minutes after the collision that the Titanic was doomed and that J.W.Andrews, representing the builders, had given him the information. Andrews had gone over the ship immediately after the crash and discovered that her hull had been ripped open. He told the Captain that the ship could not be saved."
This testimony is corroborative of that given by Samuel Hemming, a seaman, who said the boatswain woke up (sic) with the exclamation "Get out of here, you only have half an hour to live. This comes from Andrews. Keep it to yourselves."
Senator Burton planned to have Boxhall recalled to the stand before leaving for England to be questioned further about this incident.

Obviously, Boxhall was not recalled before the Senate committee.  But Burton's information formed the basis of the question asked of Boxhall in London.

Why did Boxhall profess in London that he couldn't remember when his conversation with the Captain took place?