Electric heaters are efficient in that they convert almost all of the electrical energy into heat heat energy. The downside is that it takes lots and lots of electricity, so much so that it won't be sustainable with a couple solar panels and a battery. You really should consider something like a propane Mr Buddy heater.
For a little but of electricity this is probably about what you could get for 200 pounds
That only has 240Wh which is not a lot to be honest other than some LED bulbs and charging a phone. I don't know what kind of cooler/fridge you have but it would a challenge.
Bluetti, Jackery or others sell packages that would meat your requirements, just not your budget. Search Amazon for Solar Generator if you want something all in one.
If you want to build you can by a panel, charge controller, and battery, but you'd still probably be over 200 pounds.