The insurer claims that aspects of the building work, design, components and installation of Allianz Cornhill House are defective.
Allianz also alleges that the air-conditioning system is noisy and that the building is too hot in summer and too cold in the winter.
In addition the firm claims the fire-fighting staircases do not meet British fire regulations and that the facilities provided for window cleaning are unsafe.
Mowlem started work on site in autumn 1998, with completion due by 5 November 1999. Practical completion was delayed, although Allianz moved into two floors of the building.
We are disappointed the client has felt it necessary to resort to litigation
The High Court writ says the insurer and Bride Hall agreed a certificate of practical completion, with a list of defects to be extended if any other problems came to light. Mowlem subsequently undertook several inspections and surveys and corrected defects but it is alleged that not all the problems were resolved.
In the writ Allianz argues that as the work was not finished by 21 March 2001 it reserved the right to carry out the works itself and charge.
A spokesman for Mowlem said the company was engaged in "constructive discussions" with the client and professional team.