There is no clear-cut answer to this question as there are pros and cons depending on your situation, but efficiency issues tip the balance in favour of not turning your boiler off at night.
Turning a boiler off at night means it must fire up again every morning which tends to use more energy than just leaving the boiler on overnight, especially if the temperature in your home has dropped quite dramatically. As an example, if your boiler is turned off and the temperature drops below 10°C overnight, your boiler will use more energy bringing it back up to 18-20°C in the morning than if it was just left ticking over with the thermostat at 15°C.
A more effective way of saving energy is to set your thermostat to the lowest temperature you are comfortable with so that your boiler only starts itself up when the temperature drops to that specific level.