Gemma Wilkinson, a former charity worker, took legal action in an attempt to force Anjum to reveal the whereabouts of her daughter Atiya.
Anjum, who represented himself at the latest court hearing, indicated that Atiya was in Pakistan or Iran but said he did not know her exact whereabouts.
Mr Justice Moor said he was sure Anjum was lying.
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"I saw a lot of smoke come out from the tail-end of the aircraft. I wondered if it was normal, whether it was just exhaust fumes."
The House of Commons Petitions Committee has said they will keep an eye on the petition and are concerned about fraudulent signatures.
David Cameron will be facing a hostile audience when he meets with leaders from the remaining 27 EU nations this week, writes James Mates.