In the scene just before the first large-scale battle with the English is about to start, William and his men show up. They are carrying the spears for the Scottish army to use against the British cavalry. You can clearly see there are spears already lying on the ground in front of the army.
They couldn't be fighting the British. They were fighting the English. Because the Scots are also British. So if they were fighting the British they would be fighting the English, the Welsh, the northern Irish AND the Scots!