You will need to set this up with different rules, but you can include multiple conditions in these rules. So for your 'Europe" shipping rule you can have the condition check to see if the country is a particular European country, or another.
So instead of having rules for each European country you will just have the three rules. Inside of the European rule and the rest of the world rule you will just specify the European countries each as a condition for the rule so that if it matches any of them it will trigger one or the other rule. Like you noted in the rest of the world rule you will also have to list the UK option. I'm including a screen shot of what the multiple conditions might look like as an example.
