I believe it is called Philodendron scandens.

That's what I think it is too. Daughter has one trailing off the bookcase.

Thanks both of you. I have also come up with devil's ivy or pothos but I stand to be corrected.

Mine has variegated leaves.

I have also taken several cuttings from it and given them as presents! It is a very quick grower.

I was going to suggest Pothos.

Thanks, Cottagekare. I was veering towards that myself but there is a similarity.

Happy New Year to you too, Joan! I haven't a clue about your plant but it looks lovely!

Thanks all of you. I was hoping for a definitive answer! However, you will be pleased to know that whatever they are, I have a few to give away. If you are in the South Ealing area of west London, please make contact in order to take one away. They grow very quickly and are very attractive both for the home and office!