Deer cannot be shot at night. Night is legally defined as one hour after sunset until one hour before sunrise. Any shooting of deer within of these hours can only be conducted under a specific licence.
In England and Wales there is no specific legislation prohibiting the use of any optics. So, an image intensifying (night vision or thermal) scope can legally be used to shoot deer in daylight.
The law in Scotland is different. It states that the use of light-intensifying, heat sensitive or other special sighting devices is not permitted under Section 5 of the Deer (Firearms etc.) (Scotland) Order 1985. This refers to both day and night-time usage of such optics.