The spokesman for Claudia Lawrence's family said there was "still a long way to go" in finding out what happened to the chef.
Martin Dales said in a statement:
Today has been an exacting day for Peter, his family and Claudia’s friends as the news comes of the first arrest in the five years since she went missing.
It is clear that the renewed efforts of North Yorkshire Police since last autumn and the new information provided by the public could well be bearing fruit but we shall have to wait and see.
It is vital that information continues to flow and it is to be hoped that the events of today encourage the public to keep coming forward to the police.
Anyone with information should call 101 and select North Yorkshire police if not in their area.
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Marjorie and Michael Cawdery, both 83, are understood to have been stabbed to death in a killing their family called "incomprehensible".
Detectives have launched a murder investigation following the shooting in Brent, north west London on Friday night.
Hot and humid throughout the Bank Holiday Weekend.