Head lice have been reported to live up to a maximum of 48 hours. However after eight hours they are infertile and cannot lay any more eggs. To put things into perspective though it is highly unlikely for a head louse to fall off onto a pillow, wait until you get back into bed and crawl back on. As the have claws they tend to fall off and die fairly quickly. So please no need for panic.
There is a lot of misinformation on the internet, where companies try to sell products to kill lice in the home, these are just not needed.
It is very unlikely for head lice in the UK to live more than a few hours. The most likely way aprart from hair to hair contact is sharing hair brushes, as families tend to all brush their hair on their way out. With lice still able to grab onto the hair on the brush till transported to another person head. We always advise for every family member to have their own brushes.