Do you have gas or just electricity?

Does it happen every day?

just electricity and most days

Do you have a hot water tank ?

It looks like there’s an increase of 450w or so until 9am or thereabouts. This is not ‘high’ usage but suggests that something switches on for that duration. 
If you look at 3pm and 9pm there are similar levels for a short duration so it’s a bit of detective work to find out (if those are actual readings) what switches on. 
You can start by identifying what each appliance takes in power and then check various settings (auto or otherwise). 
If you have electric heating, it could be some pre-conditioning or water heating

That looks to be something drawing 1.0kW coming on at around 03:00. Could it be a water heater? Many immersion heaters draw much more than that, but a small one might have a 1kW element. Another possibility is a forgotten electric radiator on a timer in an unused room, but I’m sure you’ve checked that. 1kW is equivalent to a one-bar electric fire, if you remember those:
  

Thinking outside the box a little, maybe something like a temprature controlled greenhouse (or garage, or even an infrared patio) heater?
Anything with a thermostatic control.
Particularly at this time of year anything with a ‘frost protection’ setting.
It can be easy to forget something like that has been switched on/left on.

Which could also explain why it doesn’t happen on some nights, warmer nights?

Maybe get up in the middle of a cold night and have a check around the whole property?

its not the hot water as thats gas heated, however i am checking to see if i have anything on a timer…..thats a great suggestion i hadnt thought of.

thank you everyone for the suggestions i will do some more investigation work and let you know!

Yes please pop back and let us know if you can @ncfishes! Brilliant advice from our Community Members, hopefully it helps you get to the bottom of it.