Who was supposed to do it is the sticking point?

There simply wasn't an organized force of British regulars within 100 miles of Philadelphia by summer 1775 and hadn't been for a year.

For several years before British CinC Thomas Gage had contracted his paltry command to major urban areas. In part to make them easier to redeploy and partly to be more visible in the face of rising tensions.

After the Boston Tea Party in 1773 and the closing if that port and the Intolerable Acts things changed more definitively.

Gage comes back from a trip back to England in mid 1774. He shifts the majority of the forces he has at hand, about 4,000 men to Boston. And he moves his HQ there from New York. And attempts to exert British power in the province. But by the end of 1774 it is VERY clear that British power extends no further than musket range from the nearest column of infantry, and even then outside Boston itself that's a dubious question.

Gage himself while respected, was both perhaps not the most decisive, and aware of the paltry nature of his force to adopt severe measures on his own terms. He also for a long time adopted the common British conception that Loyalist support was far more widespread than it was. Meaning he was reluctant to be the one escalating things.

But certain things even he could be pushed to act on. Like local militia arms stashes. But any expedition outside Boston was bound to be confronted by hostile Militia. Even if attempts in 1774 and early 75 had avoided outright warfare. These missions though required a large portion of his force though, several hundred to maybe 2k, to avoid being overwhelmed.

It was another of these local missions in April 1775 that resulted in the battles of Lexington & Concord and the proper start of the Siege of Boston.

Gage lacked the men to successfully exert Royal authority 20mi from his base. He was far overmatched to attempt to break up a rebellious assembly several hundred miles away. To say nothing of logistics like provisioning either a march overland or finding sufficient naval transports.