The route, and where it slows down
From Brockenhurst the run is A337 to the M27 at Cadnam, north on the M3 past Winchester and Basingstoke, then a short westward hop on the M25 to the airport spur. It is almost entirely motorway and covers around 85 miles.
The predictable pinch point is the M3/M25 interchange around Sunbury, which backs up from roughly 06:30 on weekdays. For a flight departing before 09:00 we normally leave Brockenhurst about three and a half hours ahead, which covers that junction as well as check-in and security.