When I spoke to the CAA on this, when you apply for your JAA licence, you get your UK one posted back as well (assuming you sent it in to convert it!).
So when you front up for your job or your local EU CAA authority, your only going to flash your JAA licence now aren't you.
How are they going to know you have a national one as well?
Who holds the JAA licence database?
Why should they care?