As a US citizen, I have long admired the UK's environmental ethos. I think that the people of the UK, living in a physically small country which must import energy resources, are more aware of their dependence on foreign energy, and consequently more willing to do things to lower that dependence. The UK also stands to suffer a great deal if climate change causes the North Atlantic Drift, a major ocean current that moderates the UK's winters, to fail or change.
The US is a very young country where people still believe that we will never run out of resources. By contrast, the UK and its people have been around long enough to know better.
Your questions was apparently presented by your instructor in terms of looking specifically at families in the UK. However, as pointed out in post #2, it should be important for all families in all countries to strive to become more energy efficient. Those same efforts should also be undertaken by individuals, companies, governments, and any other types of organizations or groups that care about the future of our planet and the living organisms on it.
I agree with the previous post. It is necessary for UK families to buy energy efficient products. As they do this, businesses will see that there is profit to be made in such products and will continue to make more of them. UK families can also vote for whichever party seems at a given time to be more likely to promote good environmental policies.
For your initial question, why, I think the answer is true of every nation:
If we (humans everywhere) do not wake up and understand that energy is not a resource we can squander, we will be left in a very dire situation very soon. I think the push for more energy efficiency occurs in most developed nations.
How can UK families become more energy efficient? Your answer there lies in small changes: use air drying instead of a dryer for clothes, change light bulbs to energy efficient ones, buy energy star appliances, develop (and FUND) better products (cars, appliances, and more) and research into those products. It's about investment: invest time and money into something and there will be output.