Tl;Dr: No such list or orders had ever been granted by Great Britain's military or its political leaders, but Britain did order that every man who stood against Great Britain be "brought to justice."
This question is strikingly similar to one that I answered last week about if Great Britain knew about the Continental Congress and ever wanted to capture the city, so I will post it right here for reference. That said, no official "most wanted" type list came out, it simply wasn't necessary. The closest thing to it that was ordered came in August of 1775 -- a few months after the hostilities between Colonial Militia in Massachusetts started and about 6 weeks after the Olive Branch Petition was sent to Great Britain.
A Royal Proclamation came from King George III. Here is the text of it below and I will embolden the important and relevant parts:
Proclamation of Rebellion August 23, 1775
A proclamation issued by George III, responding to increasing hostilities in the American colonies.
Whereas many of our subjects in divers parts of our Colonies and Plantations in North America, misled by dangerous and ill designing men, and forgetting the allegiance which they owe to the power that has protected and supported them; after various disorderly acts committed in disturbance of the publick peace, to the obstruction of lawful commerce, and to the oppression of our loyal subjects carrying on the same; have at length proceeded to open and avowed rebellion, by arraying themselves in a hostile manner, to withstand the execution of the law, and traitorously preparing, ordering and levying war against us: And whereas, there is reason to apprehend that such rebellion hath been much promoted and encouraged by the traitorous correspondence, counsels and comfort of divers wicked and desperate persons within this realm: To the end therefore, that none of our subjects may neglect or violate their duty through ignorance thereof, or through any doubt of the protection which the law will afford to their loyalty and zeal, we have thought fit, by and with the advice of our Privy Council, to issue our Royal Proclamation, hereby declaring, that not only all our Officers, civil and military, are obliged to exert their utmost endeavours to suppress such rebellion, and to bring the traitors to justice, but that all our subjects of this Realm, and the dominions thereunto belonging, are bound by law to be aiding and assisting in the suppression of such rebellion, and to disclose and make known all traitorous conspiracies and attempts against us our crown and dignity; and we do accordingly strictly charge and command all our Officers, as well civil as military, and all others our obedient and loyal subjects, to use their utmost endeavours to withstand and suppress such rebellion, and to disclose and make known all treasons and traitorous conspiracies which they shall know to be against us, our crown and dignity; and for that purpose, that they transmit to one of our principal Secretaries of State, or other proper officer, due and full information of all persons who shall be found carrying on correspondence with, or in any manner or degree aiding or abetting the persons now in open arms and rebellion against our Government, within any of our Colonies and Plantations in North America, in order to bring to condign punishment the authors, perpetrators, and abetters of such traitorous designs.
Essentially, this was an order that said that all Colonists now were duty bound to "bring to justice" or to try (as in a trial) and kill anyone who officially stood against the crown from that moment onward. Each colonial delegate from each state fully knew and understood that if the war was to fail, especially early on, it would mean that they would be executed. This also wasn't some general order, British leaders knew who were the main names who stood against them.
Just the prior month, the Olive Branch Petition had been sent to King George, and on it, listed the signed name of every man who officially led this Congress who stood against him. So with King George's new proclamation now coming out, every leader there now understood that their lives were at stake with this rebellion.