Hey there. Not to dissuade further conversation, but I just answered this question two weeks ago here. So I'll copy and paste my answer. Please let me know if you have any other follow up questions.

The King and Parliament were likely to receive of the Declaration in late August or early September 1776 at the earliest. As far as I am aware, there isn't a concise date between Revolutionary historians. That said, the official response did come on October 31st, 1776, however the initial response from the British government was Viscount Admiral Richard Howe and General William Howe about six weeks earlier, which you can see here. This document is rather short, and dismisses the 'inadmissible claim of Independency" that the colonies declared.

The British Crown's official response can be found here and like it was pointed out earlier, it was delivered on October 31st, 1776. The document asserts that King George III believed that the war was actually coming to a close and that everyone was almost ready to be friends again (which isn't true), but that these lowly colonial leaders through a wrench in everything. Here, he says:

If their Treason be suffered to take Root, much Mischief must grow from it, to the Safety of My loyal Colonies, to the Commerce of My Kingdoms, and indeed to the present System of all Europe.

King George was hellbent on trying to assert that the colonies were ruining everything and that they threatened the might, grandeur, and happiness of the entire British Empire. This is a carefully crafted speech, one that was intended to rally Parliament into agreeing to fully-fund the war since they had been reluctant to take it seriously in the beginning and as a result, had lost some pretty key battles the previous year. It also served as a war-time update to inform the MPs that Washington and his Army had been thrashed pretty badly during the August campaigns, and why fully-investing themselves into the war was worthwhile. It was meant as a battle cry against these tyrannical leaders who were not doing the will of the people, but rather, they sought to selfishly distrust the Empire's will.

Ultimately, the King and his advisors saw the Declaration of Independence as huge insult in addition to their treason. They wanted their military response to be seen in accordance of what they do to traitors (execution) and wanted to prove once and for all who held the power over these colonies.