I have an outside cooking area in the garden
(ie a heavy duty grill over a baldy spot in the grass to build the fire on) and keep charcoal, wood, and those compressed straw eco-brick things in a big plastic storage bin.
We also have a Cobb and a Kelly Kettle with all the doodads, so cooking wouldn't be a problem.
I can turn out a full roast dinner with all the trimmings over an open fire if I have to so that part doesn't worry me.
We have wind up torches, battery operated headlamps, and assorted candle lanterns, and lots of candles and tea-lights to go in them for lighting.
I keep four of those big square plastic things of bottled water stashed, and we have a rain barrel, and get plenty of rain here. I also have water purification tablets and plenty of bleach on hand.
We have hot water bottles and the world's definitive supply of fluffy blankets and onesies as we can never afford to put the heating on anyway, so that wouldn't affect us much, although in a "Day After Tomorrow" type scenario, we would have to have a fire in the living room in the Cobb and fashion a chimney from old tin cans to take the smoke out of the window. (Which I could do without much bother thankfully)
We would definitely be better off bugging in than bugging out though, and most of my plans are for bug in here.
My bug out bag (just for me, each family member has one of their own) has a change of clothes and extra warm socks, a hat and gloves, fire starting kit with wind proof matches, flint striker, and cotton wool pads soaked in vaseline in it, a small fishing kit packed into a tiny tin, a knife and whetstone, wind up torch, teeny hexamine stove and fuel, toothbrush and paste, wet wipes, paracord, box cutter, tie wraps, duct tape, superglue, and a small sewing kit.
I would also shove the family first aid kit in there if I needed it - that goes everywhere with us, and is pretty comprehensive and tailored for our needs, in it's own waterproof case.