This is really tough for the British, and they can only prevail if the militia are used aggressively. They won yesterday 5-3, losing only one complete unit (a German regular) and killing an American leader. The key was using General Barcarres to lead a militia unit to replace the lost German on the right and the failure of the Americans to advance on their right to occupy the vacated redoubts due to a lack of cards, allowing more militia to reoccupy one of them, thus freeing Barcarres and his militia unit to advance and rout an American for victory.
I understand the comment below about it being a 6-banner game. As it stands, the British can't usually afford to pursue weakened American units as to do so loses a banner for an unoccupied redoubt. Making this 6 banners at least allows a little more flexibility. Better still, award the banner for each redoubt occupied by the Americans.
The British player's woes are increased by the requirement to occupy all sections of the battlefield. In my game, it made tactical sense for one full-strength unit to screen another one with only one remaining block, but this would have meant losing a banner (and the game) for not being in the left section, which was a ludicrous position to be faced with. We played by the rule, but the British were saved only by the American lack of an appropriate card. I think this rule should be dropped.
Finally, there is an error in the battlefield screenshot above. According to the printed rulebook, one of the light units with Morgan should be a rifle unit.