Ttdfjt

When did Britain learn about the American Declaration of Independence?

We all know the declaration was made on July 4th, 1776. But when did news reach Buckingham Palace and do we have records of their reaction to it?

The news reached London on the 10th of August. It was, of course, known by British officials in the colonies much earlier, but

It is astonishing how casually the Declaration was first reported to
official London. On July 8 ex-Governor Tryon in New York wrote to
Lord George Germain, the colonial secretary, and Admiral Shuldham
wrote to the Admiralty Office, but neither of them made any reference
to the momentous document. On the same day General Howe also wrote to
Lord Germain, and buried in his letter is the brief sentence: 'I am
informed that the Continental Congress have declared the United
Colonies Free and Independent States.' That was all, as if he were
reporting that Congress had recessed or had issued some new currency.
These three letters reached London on August 10, making very good time
crossing the Atlantic.

Source: H. Peckham, Independence: The View from Britain (Proceedings of the American Antiquarian Society, October 1975, Volume 85, Part 2)

As called2voyage and T.E.D. have pointed out in their comments, Mr. Peckham should not be astonished by this, and the author himself notes that

At least two pamphlets had appeared earlier in the summer predicting
that the colonies were going to separate themselves from the crown.

Granted, the pamphlets were not quite the same thing but then the two sides were already at war (see also T.E.D.'s answer). On the declaration itself:

...by the middle of August a copy of the Declaration did reach London
by some other means, as it was completely printed in The London
Chronicle under date of August 16, although that issue of the paper
appeared on the 17th or 18th. The British ministers and King George
now all had a chance to read the forthright statement and react to it.

Source: H. Peckham

Also,

The St. James's Chronicle (London) for August 15-17 printed the
Declaration in full, but with some curious editing to protect the
king's name. In the second paragraph, where it reads 'The History
of the present King of Great-Britain,' the wording has been changed to
read: 'The present History of Great-Britain.' This omission of the king
then makes it possible to change all the charges leveled against him
from 'he' to 'it,' referring to Great Britain rather than the monarch.

On the reaction of the monarch and the government,

Official reaction did not yet manifest itself. Parliament was in its
long summer recess, and most of His Majesty's ministers were out of
London at their country residences. They did not feel compelled to
issue statements, and as a matter of fact they looked upon the
Declaration as a kind of dying gasp from a revolutionary force that
was expiring. The military situation made them optimistic.... The rebellion couldn't
last.

Source: H. Peckham

The British government reacted by hiring

John Lind, an English politician and pamphleteer,
to write a rebuttal to the declaration. He wrote Answer to the
Declaration of the American Congress, a reply that tried to pick apart
the Declaration of Independence. Lind focused on the issue of slavery,
saying that the colonists were actually angry that King George III had
offered freedom to the slaves....

Following this, King George III officially declared the colonies to be
in a state of rebellion. By August of 1776, the King ordered troops to
the colonies.

Not until October 31st did the king speak before parliament:

In his address, the king spoke about the signing of the U.S.
Declaration of Independence and the revolutionary leaders who signed
it, saying, “for daring and desperate is the spirit of those leaders,
whose object has always been dominion and power, that they have now
openly renounced all allegiance to the crown, and all political
connection with this country.” The king went on to inform Parliament
of the successful British victory over General George Washington and
the Continental Army at the Battle of Long Island on August 27, 1776,
but warned them that, “notwithstanding the fair prospect, it was
necessary to prepare for another campaign.”

Not repeating info in the other answer(s), but it should be realized that by the time the Declaration of Independence was written, the Battles of Lexington and Concord were already more than a year old (April 19, 1775), as was the Colonials' Continental Army (June 1775).

Parliament in London by this time was already quite certain they had an organized revolt on their hands. In fact, Parliament had declared Massachusetts colony to be in rebellion back in February of 1775. That is before either of those above two events, you might notice. In fact, its tough to read the entire history of the dispute and not come away with the feeling that the Colonists weren't really driving it at all. Rather it seems as if Parliament slowly dragged them into more and more extreme positions. If anything it was the colonists who were finally recognizing and admitting to the truth of the situation in 1776.

Parliament at the time was run by the more authoritarian Tory party¹. They were pretty consistent during the entire history of the dispute with the American colonies in reacting to every setback by doubling down on their position. This was great for getting them re-elected back in England, but not so great for solving the actual problem. A pretty good book on the politics of the British side of things is Barbara Tuchman's March of Folly.

So the Declaration of Independence shouldn't be viewed as having started anything², but rather as a statement of justification and intent by the colonials for the war they had already been fighting for well over a year.

^{1 - I'm talking about the 18th Century Tories here, not the 21st Century ones.}

^{2 - Official birthdate of the nation aside, of course.}