There are fears a legal loophole could allow cloning
This is despite cross-party concern about the speed with which ministers are acting; the bill cleared its Lords stages after only a five-hour debate on Monday.
The hasty move through the parliamentary process follows the claim at the weekend by US scientists that they had managed to create the world's first human embryo clones.
Legal loophole
The UK legislation is designed to close a recently exposed loophole in the current law, which ministers fear could be used to justify unlicensed cloning experiments.
Junior health minister Hazel Blears emphasised the need for urgency in pushing through the fast-track legislation.
"Bringing this bill forward reflects the concerns raised frequently by Parliament and the public about the importance of ensuring reproductive cloning cannot take place in the United Kingdom," she said.
Tory backbenchers, led by former ministers Ann Widdecombe and Edward Leigh, attempted to block a second reading because the bill did not prevent the creation of all embryos by cell nuclear replacement; it would still permit the creation of embryo clones to develop new transplant therapies - so-called therapeutic cloning.
However, the Tory blocking manoeuvre was defeated by 288 to 49, a majority of 239. The bill then went through its second and third readings unopposed.
Further legislation
Shadow health secretary Liam Fox said Tories had been given a free vote on the bill, but he called the drafting a "stop-gap measure".
"Even many who will support the government today, while supporting their aims, have grave doubts about the government's competence on this matter and will require further legislation before our fears are laid to rest."
For Liberal Democrats, Dr Evan Harris backed the ban but also warned further legislation would be needed.
Ministers were prompted into action when anti-abortion campaigners, the Pro-Life Alliance, won a High Court ruling that laid bare a deficiency in the legislation covering embryology research.
This flaw centred on the legal definition of an embryo - the union of an egg and a sperm. Because a clone is produced in a different way, the judge ruled current regulations did not embrace the new technology.
Pro-life groups want both reproductive and therapeutic cloning banned.