There are fears a legal loophole could allow cloning
The development was being hailed by some as an incredible scientific achievement and others as a dangerous step.
The UK legislation was drawn up by the government to close a recently exposed loophole in the current law, which ministers fear could be used to justify unlicensed cloning experiments.
The bill was only published last Thursday, has its Second Reading in the Lords on Monday and should finish all stages in the Commons by the end of the week.
Court ruling
It makes it a criminal offence "to place in the womb of a woman a human embryo that has been created other than by fertilisation".
The government action was deemed necessary after anti-abortion campaigners, the Pro-Life Alliance, won a High Court ruling that laid bare a major 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 that current regulations did not embrace the new technology.
This loophole, in theory, could allow someone to conduct cloning experiments without the licensed permission of the Human Fertilization and Embryology Authority, the body that is supposed to oversee this area of research.
Therapeutic cloning
In reality, commentators said, other laws relating to medical malpractice and even assault could be used to prevent cloning experiments.
Nevertheless, the government is determined to remove the legal flaw. It also intends to appeal against the High Court ruling.
Ministers hope that by closing the loophole researchers will then be properly licensed to carry out a more limited form of cloning - so-called therapeutic cloning - that aims to develop replacement cells to treat degenerative diseases.
The government's critics say the country's embryology legislation is deeply flawed and there is little point in merely trying to patch it up.
They want both reproductive and therapeutic cloning banned.