You can rent aircraft or buy an aircraft in the UK and fly it on your FAA PPL. You would need a checkout on a rental aircraft and insurance if you buy an aircraft, but other than that I believe you can fly indefinitly on the FAA Private Licence.
I believe you cant fly at night though, just day VFR. I'm sure someone will correct me if this is incorrect.
Also you can only legally fly a G- registered aircraft on an FAA licence while in the UK, ie you cant take it to France etc.
Whether the rules are the same in France and Italy I dont know.
If you were to gain an FAA commercial license etc this gains you nothing for flying in the UK if you are flying a G- registered aircraft. Even if you have an ATP, you can only use the Private privalidges on a G- reg aircraft.
Of course there are some N reg aircraft over here, which you could fly using an FAA IR.
As far as operating commercially though, you would have to obtain an Air Operator Certificate and that would be more difficult, particularly if you intended operating an N reg aircraft with FAA licence. You would also have to have the right to work in the UK or whatever country you chose.