I think that most of the blame lies with General Howe. General Burgoyne does share some of the blame as well because of the miscommunication after leaving New York. I do not believe the ministers in London have any blame for a swift victory. I do however think they could be blamed for more Colonist joining the cause because of the Coercive Acts of 1774.
Early in the war the focus by General Howe was not to destroy the rebel forces. He just wanted to quell the revolt. General Washington did a good job of not becoming decisively engaged giving Howe the opportunity to completely