The Whig party in Britain was largely sympathetic to the complaints of the American revolutionaries, opposing the Coersive (or Intolerable) Acts and generally favoring a negotiated settlement. There's a reason the terms "Whig" and "Tory" were used in America to refer to supporters and opponents of the revolution.
Have the Whigs do considerably better in the 1774 elections. Not an outright majority, or you're likely to butterfly away the Revolution until several years later, but just a few seats short of a majority. That way, it would be much harder to pass bills funding the war (both operations and the cost of expanding the army with recruits and mercenaries), and a major setback such as the loss of the Siege of Boston (March 1776 IOTL) might get enough MPs to reconsider their views and join the Whigs in opposing the war. If that happens, the Continental Congress would begin receiving serious peace overtures right around when IOTL they were starting to debate declaring independence.