Twenty other Greenpeace members who were arrested at the site in Lyng, Norfolk at5.30am on Monday also had their applications for bail turned down by Frazer Morrison, the stipendiary magistrate, at Norwich yesterday.
The decision on Lord Melchett, 51, means he will miss a pre-booked holiday due to start today and lasting more than two weeks in Tanzania with his family. His lawyer said that he was "anxious to go".
The decision to hold him in custody came after Nick Methold, for the prosecution, said it was the Crown's belief that the defendants would all reoffend if granted bail, following a "highly sophisticated and well organised" act.
He added that Greenpeace's stated policy was to destroy GM crops before they flowered.
Mike Schwartz, for Lord Melchett, had asked for his release on the basis that the tickets for the holiday were already booked and the length of the holiday would take him past the GM crops' flowering time. But Mr Morrison refused bail on the grounds that the defendant was likely to commit another offence and because of the nature of the offence itself.
The arrests of Lord Melchett and the other Greenpeace members followed the destruction of about half of a six-acre crop of GM maize at Walnut Tree Farm in Lyng, near Norwich. The crops were destroyed by a tractor and cutter.
The site is one of five remaining farm-scale trials of GM products which the Government has said must take place before it will approve commercial growing of GM crops. Scientists are now evaluating the damage to the crop to determine whether any results from the trial are valid.
The value of the damage was estimated at pounds 750.
Lord Melchett entered no plea against charges of theft and criminal damage during the 20-minute hearing. Greenpeace later said all those charged - aged between 21 and 57 - would plead not guilty.
Earlier, Lord Melchett said: "The British public have made it very clear they do not want these GM farm-scale plans to go ahead. It is vital that the crop is removed before it flowers, spreading GM pollution."
Speaking on BBC radio, Mr Schwartz said: "Greenpeace's view is that something needs to be done about the threat of GM crops and the authorities are not (taking) and cannot take the correct action, so someone has to do it - and unfortunately it has fallen to Greenpeace to protect everyone's interests."
Greenpeace has published on a website details of the locations of the other four trials:
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