In the "In the Shadow of the Hill" scenarios (4 separate scenarios) I cover a Brigade attack, with the map based on google earth and period maps and the forces at play are as accurate to reality as the game will allow. This shows how the forces were made up based on AAR documents and in all cases the various battalions attacked with only two companies up and with armour and artillery support.
If you look at the scenarios in detail you will get a good idea of the tasks allocated to the three battalions (4th Dorset's, 5th Dorset, and 7th Hampshire's)
mission 1 & 2: C & D Co 5th Dorset's, plus supporting arms (armour and artillery) are tasked to capture two farm complexes
mission 3 : A & B Co 4th Dorset's, plus support are tasked to capture a small village.
mission 4: A & B Co 7th Hamp's are tasked to capture a further village.
As shown below each action allowed the next to take place, allowing the Bde to move forward in bounds as it secured it's objectives in turn. Each battalion had roles within the Bde plan, while each company had a role in it's respective battalions plan, (and each platoon within each co and so on)
The master map for these scenarios is 1.6k wide by 4k deep, with the first three missions seeing the forces needing to cover 1.6-2k, with a similar distance covered in mission 4 albeit the start line for the advance is 2k deep into the master map.
These missions are very histrionically accurate in terms of the terrain and British forces involved, and so give some insight into what was asked of the actual units on 10th July 1944