The British were firing while they were marching forward. Standard practice was to halt and then fire.
When the British were fighting against a group of militia, no one gave a command to fire, but they fired anyway. The British then initiated a charge, again without an order given. The British Army of the 18th Century was well disciplined and would never break discipline by acting without orders.
When the patriots crouch behind the stone walls of the road leading away from Concord to ambush the British, one of the Americans brushes against a stone wall and it moves.
At the Battle of Lexington, the Regulars did indeed break rank and fire without orders - historical fact. They fired after a single musket went off - although many said it was a pistol. The tension that had been building exploded and the soldiers broke ranks and fired - and they also fired while advancing - some chasing the militia a half mile to the Hancock/Clark House.
The rider spreading the alarm that the British Regulars were on their way pronounced the name of the town Concord as "Conn-chord" while most of the rest of the cast correctly pronounced it as "Con-curd".