Lawyers representing a woman who is among 23 being held as part of the inquiry into an alleged bomb plot have applied for a judicial review.
The women is one of 23 people currently being held
Representatives of the woman known as "J" say she is being held unlawfully because a judge did not explain why he extended her detention.
She has an eight-month-old baby and is being held in connection to an alleged plot to blow up transatlantic airlines.
Her custody was extended on 16 August and is due to expire on Wednesday.
Her husband is also in custody and their baby is being cared for by relatives.
Extensions to the woman's custody were granted on 11 and 16 August.
She is being held on suspicion of involvement in "conspiracy to use a liquid explosive on airline flights".
ARRESTS OVER 'BOMB PLOT'
10 August: 24 people arrested in London, High Wycombe in Buckinghamshire, and Birmingham
11 August: One released by police without charge
15 August: Another person arrested in Thames Valley area
16 August: Police given extra time to question suspects; one person held in Thames Valley area released without charge
21 August: Police have until this date to question two of the suspects arrested on 10 August
23 August: Police have until this date to question 21 of the suspects arrested on 10 August
Her lawyers are arguing that her detention is unlawful because the senior district judge did not give reasons for granting the extensions, even though the Human Rights Act stipulates that judges must give reasons for their decisions.
The judge only said "the investigation is being carried out expeditiously and diligently".
The suspect's legal team said the provisions made under the Human Rights Act provide a "fundamental safeguard".
Her lawyers say J "has shown a more than arguable case. Her detention is unlawful".
The case is expected to go before Mr Justice Collins at the High Court on Monday afternoon.
Officers have been granted an extension until Wednesday to question 21 of the 23 people being held. They will need to apply for a further extension if they wish to hold another two people beyond Monday.