Yes, it certainly did happen.

Danbury, Connecticut: April 26, 1777 the British burned the American supplies at Danbury. According to Gen Howe's report, they destroyed;

A quantity of ordnance stores, with iron, etc.; 4000 barrels of beef and port; 1000 barrels of flour; 100 large tierces of biscuit; 89 barrels of rice; 120 puncheons of rum; several large stores of wheat, oats, and Indian corn, in bulk, the quantity thereof could not possibly be ascertained; 30 pipes of wine; 100 hogsheads of sugar; 50 ditto of molasses; 20 casks of coffee; 15 large casks filled with medicines of all kinds; 10 barrels of saltpeter; 1020 tents and marquees; a number of iron boilers; a large quantity of hospital bedding; engineers’, pioneers’, and carpenters’ tools; a printing-press complete; tar, tallow, etc.; 5000 pairs of shoes and stockings. At a mill between Ridgebury and Ridgefield, 100 barrels of flour and a quantity of Indian corn.

Not content there, they burned the private homes as well before moving back to their ships. The burning of Danbury would cause a small force under Gen Arnold and Gen Wooster to pursue the British, Wooster being fatally wounded in the skirmish. Arnold would continue to pepper the English ranks during their withdrawl but never inflicting heavy losses.

Kingston, New York: October 1777, troops from New York March north and enter Kingston which housed New York's constitutional convention where Jay authored the document establishing their state government. As revenge for aiding their congress, every building in town was burned.

Fairfield, Connecticut: July 1779 citizens are notified British troops are making landfall nearby. Citizens secure livestock, hide valuables, and make a choice to stay and hope for the best, flea, or defend the town. Citizens gathered at Black Rock Fort to make a stand and repelled the assault of General Tyron. Reinforcements under Gen Garth were brought to attack the fort from the rear but this was anticipated: The colonists had burned a bridge leading to the fort, so Garth burned Fairfield in retaliation. Several citizens were killed in the razing of Fairfield. They burned homes, barns, sheds, churches - everything they could as they withdrew. After they burned his home, the Reverend Andrew Eliot said the soldiers were the

the vilest ever let loose among men.

George Washington, upon seeing the town in 1789, said

The destructive evidences of British cruelty are yet visible both in Norwalk and Fairfield; as there are the chimneys of many burnt houses standing in them yet

Richmond, Virginia: Jan 1781 Arnold, now with the British army, invades Virginia burning settlements all the way to Richmond.

There are numerous examples beyond these of brutal violence and what we would now define as war crimes against the colonial population. Rape occured. Looting was very common. It was so extensive that in 1777 congress would form a committee to investigate the attrocities. A young Andrew Jackson would wear a scar from an officers saber for the rest of his life. He was told as a POW to polish an officers boots and refused, so the officer hit him in the face with a sword.

Great resource on British (and American) brutality in the revolution: Scars of Independence: America’s Violent Birth, Holger Hoock