This is probably a moronic question but after defeating a map (taking all bases) in a campaign how can I go to the next map? I tried clicking different things including stuff on the map view (including world minimap) but no elements seem to be clickable and nothing ever happens.

There are special 'exit' markers, You just walk into one. Look for them at the map, they have names like 'To Fridge Valley' or 'To Vigil Island' and so on.