Outside of the house that will suit your needs (but may not be what you have dreamt you will be living in since you heard you were going to be living the UK), you MUST look at the Energy Performance Certification (EPC) rating. This is going to tell you how much running the house will cost you, this is how you can save money on energy because it costs 3 times as much as in the US.
Any house that is sold or rented out must have an EPC. Most advertisements will have the rating of the house in them. The ratings go from A to G. A is the most efficient and G is the worst. The average one is D/E and if you are in the military, your utility allowance should cover a home with this rating. Here is an example of what an EPC looks like. If it does not have it in the advertisement, I would be weary of the property and ask to get a copy of it before viewing.
One thing to look for in a house, always go for double glazing. I have been living in a house for the last 3 years that does not have it in the bedrooms (its my MIL's house) and they have been just been installed, you can feel the difference now in the spring but just imagine the difference it will make in the winter- we were sleeping under 4 blankets! Please see the video below to see the impact that this can have.
Another thing to think about is other heating elements. Fireplaces are another way to heat your home. Just be sure to only use coal in a coal one and wood in a wood one. Wood burners are more energy efficient than coal burning ones. If you do get other heating elements like space heaters, make sure that they have timers on them and do not leave them running when you are not home. Do not heat rooms you do not use.
You can also look in the report to see the suggestions made to increase the EPC rating, therefore saving you money on your utilities. Things like replacing regular lightbulbs with energy saving lightbulbs you can do yourself. Although they are more expensive than regular ones definitely save you money in the long run. Other things like increasing the loft insulation or having the hot water cylinder insulated could be a good negotiating point especially if you are paying above the asking price.
As Americans, we like to have our homes very warm but this can cost an arm and a leg over here. So dress warmly in the cold times and put a blanket over you when watching TV. This is why I think that you should choose a home with a better EPC rating almost anything else. You will feel the difference in your bones (the humidity makes the chill way different here) and you will feel it in your wallet.