US Presidential elections are indirect: the people vote for an electoral college and the electoral college votes for the President. States assign electors in a winner-takes-all manner (either state-wide or per district), which leads to the campaign being focused on swing states. In United Kingdom parliamentary elections, each constituency elects one MP in a first-past-the-post system. Many constituencies are virtually certain to remain with a particular party (safe seats).
In both cases, I could imagine that someone living in a safe state or safe seat may be less motivated to vote, than someone living in a swing state or marginal seat. Is there any evidence that turnout is higher in swing states than in safe states, and/or higher in marginal seats than in safe seats?