Anonymous but potentially vital information posted on the social networking site Facebook is frustrating police investigating the disappearance of Claudia Lawrence.

More than 30,000 people have joined dedicated internet groups swapping thousands of messages discussing the mystery of the missing university chef, who was last seen leaving her home in York a month ago.

Many postings amount to little more than crackpot theories and lurid conjecture. But North Yorkshire police intelligence officers monitoring the websites have uncovered tantalising leads which they are unable to pursue because they are logged under nicknames or sent from public computers.

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They are among hundreds of fresh posts added each day to the dozen or so different user groups originally set up by friends to aid the search but now swamped by people from all over the world deeply touched by the plight of the Lawrence family. As he revealed two "very significant" developments in the search for the missing 35-year-old, Detective Superintendent Ray Galloway said he welcomed any information that would help him make a breakthrough but admitted the scale of response to the viral appeal on the internet was difficult to manage.

He urged anyone who knew anything that might help to contact the police. "That [social networking sites] is the way young people communicate," said Det Supt Galloway. "They are willing to impart information there in what they feel is a safe environment. I want to assure them the police is a safe environment as well and we might be able to help Claudia."

Some members of the public joining the internet groups have said that they know Ms Lawrence but police are unable to corroborate or "contextualise" the claims.

Piecing together her personal life has been central to the efforts of the 50 officers investigating the case. Det Supt Galloway believes the woman knew her suspected abductor. But he said mounting conjecture that her private life was "more complex" than her family or friends knew was irrelevant to the task of finding her. "I want to know all about Claudia," he said. "I want to know all about her relationships, not to judge them." He said there was no evidence of a new relationship in her life prior to her disappearance.

Police also revealed that a motorist spotted a couple having an argument near York University's Goodricke College at 6.10am on 19 March, close to where Ms Lawrence last made contact with friends and family 10 hours earlier. He said the fact that the passenger door of the car was open indicated that the woman may have been in the car and knew the driver, though was no description of either the couple or the car.

In another potentially significant development, it emerged that two men had been spotted outside Ms Lawrence's home in the Heworth area of York several days before she went missing. Police have already questioned friends and associates of Ms Lawrence and searched waste ground, sewers and rivers. Posters showing her smiling face can be seen on shops, pubs and clubs throughout the city of York. Ms Lawrence's father, Peter, a solicitor from Malton, North Yorkshire, has made a series of emotional appeals pleading for information over her whereabouts. The Archbishop of York, Dr John Sentamu, has also led prayers for her safe return.