differential play

I have taken the two drive shafts off as part of dismantling the car ready for a new chassis. I find that i can move the rear diff about 15% forwards to back by hand before it engages.
I have about the same amount of play on the front diff.
I can't find a specification of what amount of play is normal or acceptable. If this is more than is reasonable, is it possible to fix this at home, or do I need to hand it over to a specialist?

They are like a prick in a bucket!
In fact pretty much all the LR live axle diffs are much the same.

If you mean 15 degrees of movement out of 360 that's pretty good.