Ian,
I do not claim to be a gunsmith but for what it is worth, if your ammunition has thin rims and thus is not held by the chamber next to/touching the breach, the thin rims are likely the problem.
A simple test might be to point the muzzles toward the sky and fire a few shots in each barrel. To ensure a controlled test only load one barrel for each shot. While loading keep the muzzles SAFELY elevated. The weight of the shell should keep it resting against the breach.
If the shells all fire in the above test them the porblem is likely the thin rims of the shells. Perhaps someone else will have a solution to this problem.
PS: I didn't remember where Zambia was so I Googled it:
http://en.wikipedia.org/wiki/Zambia
I take great pride that the PGCA can via the Internet be accessable to an entire world of Parker shooters and collectors!!!
Respectfully,
Mark