LONDON (Reuters) - Cohabiting couples should not have the same rights as married couples or civil partners, but those with children or who have lived together for some time should have legal protection, the Law Commission says.

The Commission, an independent body that advises the government on the need for legal reforms, said its proposals would not undermine marriage but provide fairer financial outcomes for cohabiting couples after a break-up or death.

Many cohabitants mistakenly believe in a "common law marriage myth," meaning that they would be treated the same as married couples, the Commission said.

Its report said current rules that applied to unmarried couples were unsatisfactory and needed reform, often leading to "unjust outcomes", particularly for children, when relationships ended.

The Commission said the scheme it recommended would only apply to those with children or a couple who had lived together for a minimum length of time, suggesting from two to five years.

The two-year study, however, concluded that the breakdown of a cohabitant's relationship should not be treated the same as divorce.

"Many people think that cohabitants should have access to exactly the same remedies as married couples and civil partners. We do not agree," the Commission said in a report.

The 2001 census found there were more than two million cohabiting couples in England and Wales.

However suggestions these relationships should be given legal status, first mooted last year, led to criticism from the Archbishop of Canterbury Rowan Williams who said it would lead to the erosion of marriage and muddle its role in society.