You’re getting closer. Defining it in terms that you have will work for the purposes of this rule.
The UK ships, and all of their other units for that matter, are controlled by one unified UK. The terms Europe economy and Pacific economy are only relevant when it comes to purchasing and placing units and making repairs to facilities. After the purchase and repair phase of the UK’s turn, all of the units move and fight as one power. On the place units phase and collect income phase, then the “economies” are separated again.