Fatigue,
OK, in the UK all police helicopters are available to fly at least some of the night. Fundamentally, this is because there is a demand for them from the ground troops, and a history of great results at night. In this respect, the UK is the same as anywhere else.
UK air ambulances in the primary role are not allowed, in practice, to land at the scenes of accidents/casualties at night, so there is not much point in them being available after it gets dark. The exception is (or used to be) the NHS-funded helicopters in Scotland, as they are used for inter-airfield transfers with lights etc. at night
Helicopter HEMS could be equipped to do landings at night off-airfield (IFR fit, means of checking the site at night etc.) but it all costs extra that the charities that pay for HEMS cannot afford, and would reduce the spare payload, so pushing them to bigger and more expensive helicopters that they cannot afford........