From the A14 / M11 southbound, you cannot exit at Junction 13.
This is generously wide but only marked two lane - overtaking can thus be hairy, especially southbound, up the hill.
Turn right and join the A720 city bypass southbound.
However Park Lane will be closed southbound between 0830 and approx 1300 for a parade at 1200.
The first section runs southbound through the New Forest, with plenty of shade on a hot day.