If you're after a middle-ground sort of route that avoids busy Southampton Way, I recommend going through the housing estates.
Here's a map: [g.co
At the bottom of Lyndhurst Way, head straight across to go down Kelly Avenue. (the road has a barrier but space for cycles down each side). Turn left at the bottom on to Commercial Way, then hang the (third I think) right into Chandler Way. Again there are some bollards on the road's entrance but not a problem for bikes.
Then it's straight down to St George's Way, turn left and then right at the lights.
Not as fast as just going down Southampton Way, but it's much quieter which, to me, is more pleasant. You can get a clear run without dodging buses and weaving round traffic jams (though it does get busy along St George's Way waiting for the lights)