what is the quickest way to drive from SE London to Dorchester?

[Mercedes]

We're driving down tomorrow during the day to Tolpuddle, near Dorchester. Last year I drove through Lewisham out to Croydon, then on M25 and then on to the motorway down to Sothampton etc. It took about 6 hours as getting out to the motorway was horrendous and then we got stuck in a jam outside Winchester for ages.
Does anybody have any suggestions or routes that would decrease the journey?
Friends last year took a cut off to Salisbury and didn't go down the motoroway which they said is quicker even though its not such a fast road.
The AA route master says it should only take 3 hours by my original way which made me laugh.
Desperate for advice as I will have dc in back of car.

I'd go M25, A303 then probably cut off either at Salisbury onto the A354 or if not, come off the A303 to Yeovil and down to Dorchester on the A37 and then go east the short distance on the A35 to Tolpuddle.Never a good journey no matter which way you go!!!

We go regularly from W London. A316, M3, M27, A35. Sometimes it's 2 hours (to Bridport, 17 miles beyond Dorchester) sometimes 4+ depending on traffic. Beware of rush hour at Southampton/Bournemouth.

After motorway ends you're at the mercy of tractors and caravans on the single carriageways.

Don't believe there's an easier way, good luck. We only ever try it at night so kids will sleep