The IAA would pull an IAA JAA PPL upon gaining the IAA JAA CPL, not sure about the UK one. Try to find the appropriate regulation, print it out and don't mention it anywhere if it allows you to hold both.
If it does not, better to give it up rather than taking the risk... You will get a new FAA PPL issued for your IAA JAA CPL (so I believe).
Hope that helps. IP