http://www.nationalcarshare.co.uk/
"Lift sharing", "ride-sharing", "car-sharing" or "carpooling" -it doesn't matter what you call it, it boils down to the same thing - two or more people sharing a car to get from A to B rather than driving alone.

http://www.freewheelers.co.uk/
Login and Travel
To access contact information for other Freewheelers lift sharers. But you must register below first.

http://share-a-lift.co.uk/ and then go to FAQ
What is lift sharing?
It is when two or more people decide to travel to work together in one car rather than separately. It is really aimed at getting vehicles off the roads by increasing the number of people in each car.

http://en.wikipedia.org/wiki/Liftshare
Carpooling (also known as car-sharing, ride-sharing, lift-sharing and covoiturage), is the sharing of car journeys so that more than one person travels in a car.

https://www.liftshare.com/faq.asp?skin=377
What is car-sharing? (liftsharing, ridesharing, carpooling)
Car-sharing (also called liftsharing, ridesharing and carpooling) is when two or more people share a car and travel together. It allows individuals to benefit from the convenience of the car, whilst reducing the costs and alleviating the associated problems of congestion and pollution.

http://www.234car.com/
234car matches fellow travellers and allows them to find the best people to share their journeys. Whether you call it car sharing, lift sharing or ride sharing - 234car is the most advanced solution available.

http://de.wikipedia.org/wiki/Fahrgemeinschaft
Eine Fahrgemeinschaft ist eine Gruppe von zwei oder mehreren Personen, von denen eine mit dem eigenen Auto die anderen zum Arbeitsplatz oder auf eine Fahrt mitnimmt. Fahrgemeinschaften werden privat organisiert oder in Mitfahrportalen im Internet zusammengesucht.

I'm German, but living in the UK for 7 years.
When my brother asked me yesterday what lift sharing is, I was really surprised that none of the dictionaries contains "lift share".
In our company we regularly use the terms "I'm having a lift share" or "I'm lift sharing with someone". We also use the term "my lift share" for the other person who is lift sharing with me.
The personnel department is regularly sending emails around that the company is promoting lift sharing or that someone is looking for a lift share.

Please can some native (British) English speakers confirm that "lift share" is commonly used in England and that they support adding it to LEO.