Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from Bangor, Maine to United Kingdom as you normally would.
Due to multiple factors, expect to potentially pay more when booking in June. For low rates, March can be a great choice for travel to United Kingdom. Flights to United Kingdom from Bangor, Maine in March are about $1,072 on average during March, but can be found for as low as $565.