Occasionally the Government will offer a Bill to a backbench MP to take forward as a Private Members' Bill. This is known as a Hand-out Bill. These are usually Bills for which the Government has not been able to find time in its programme or, for some other reason, it does not want to present itself. Since such Bills come with government support, they stand a good chance of becoming law and are often taken up.
Further information on this subject can be found from the following link.
House of Commons Information Office factsheet: Private Members' Bills Procedure