Lightning Boy
There is no problem with converting an FAA PPL to a JAR PPL, but there are some requirements that must be met for license issue.
You must have at least a JAR class 2 medical, you must pass the current PPL air law exam, and the PPL skills test.
How much training you ay require to do this will be a matter to be assessed by your instructor, as there are differences between the 2 syllabi.
In general though provided you have been taught thoroughly for your FAA license, and do sufficient dual to become familiar with UK airspace and procedures, you will not have a problem.