differential or gear box noise help | PUBLIC ENQUIRIES | Forum

Morning all I am hoping for some mechanical advice please . the car in question is a Wolseley 1500 . The car drives lovely changes gear lovely but there is a thud noise coming from under the car. The noise is mainly after changing in 2nd and 4th gear but can be replicated by taking your foot of the accelerator allowing car to slow a bit then reapplying your foot to the accelerator. It definitely sounds as if coming through the floor from the rear of the car.
Engine mounts checked
Gear box mounts replaced
Half shafts checked
Rear diff removed checked some backlash but within tolerance
Diff oil replaced which gave marginal improvement in noise.
We are at a total loss now as to the actual cause could it be the gearbox all along or is it originating from the differential .
I can’t afford the expense of having the rear differential sent off and overhauled only to find it is the gear box that needs attention instead .
I am in Wiltshire and any advice or experience of this will be very much appreciated.