Two suggestions. One is to take the m11 then left on the the 505, right at the next roundabout down to Newport. There's a left turn in Newport that will lead you on back roads through Debden, Thaxted, Great Bardfield, Finchingfield, Castle Hedingham and on to Sudbury. Great roads.
Or stay on the A14 to the Quy junction, and make you way to Fulbourn. From there you do Balsham, Ashton, Finchingfield and then as before.
Can't really recommend the route from Haverhill or Clare to Long Melford: too much traffic and too many speed limits. If you really want a shorter rote then you'll have to be prepared to pick your way through the villages. A sat nav is essential cos none of the roads go in your direction for long. Something like this: leave the A14 at Quy and follow the signs right into Newmarket where you take the right turn to Dalham. Then head towards Stradishall, but just before you reach the village take a left and head for Boxted. You'll end up on a lane that will take you down to the A1092 where you turn left to Long Melford. Right in Melford on the main drag where an easily-missed left hand shortly after the Hall takes you to the junction for Acton.
Have fun!