I have tried to isolate the offending "Drain" by checking the meter readings overnight after I have switched off the appliances still normally operating, i.e. The Fridge/Freezer in the kitchen, the Freezer in the Garage, the Security Light, The House Alarm system and still getting 4 Units of electricity consumed!
If that is the case, then, as you go on to say, getting a plug-in monitor would not help you. The whole point of that was to ascertain which of the suspect aplliances (fridge/freezer and freezer) was using an excessive amount of power.
Do I take it from what you now say that, as far as you are concerned/aware, there was
absolutely nothing meant to be using electricity (apart, perhaps, from the occasional light) during that night when the meter still showed 4 units consumption?
As has been pointed out, 4 units overnight represents a continuous load of about 500W, which is far from insignificant and hardly likely to relate to something that has been 'overlooked' - it would really have to be something that produces heat, one way or another. You didn't mention an immersion heater (which is something that has been mentioned before) - do I take it that there is not one (even one which you weren't aware of, or didn't think was being used)? Possibilities like greenhouse/loft heaters and high-powered garden lights have already mentioned - I assume that there are none of those?
You could, I suppose, systematically work your way through your consumer unit, switching each circuit off, one at a time, overnight in the hope that this will enable you to narrow things down to one circuit. (if you did that, start with the socket circuits, and leave the lighting ones until last). Ultimately, if you could cope without any electricity (even lights) overnight, you could switch off the entire CU overnight - if the meter was then still showing consumption, there would then be very few options left (although, I confess, I've never heard of a meter showing appreciable consumption when there is none at all!).
Kind Regards, John