The writ comes after the cost of the refurbishment work on the house doubled to more than £11m.
In the writ, served by lawyer Berrymans Lace Mawer, Durtnell is seeking an injunction banning Kaduna from further development on an adjacent field and properties.
Durtnell and Sons started work on the project in 1999 and claim the original 60-week contract was extended by architects' certificates to 85 weeks.
The writ claims that by the end of November 2002, the contractor had been on site for 180 weeks and that escalating costs prompted disputes between the contractors and property company Kaduna, resulting in adjudication.
An adjudicator awarded Durtnell payment of £1,228,313 on Christmas Eve last year, but Kaduna has refused to pay the money. Kaduna has also not paid an additional £60,434 awarded to the contractor by the project architects, claiming it was entitled to set off liquidated and ascertained damages against this sum because the scheme had not been completed and a certificate of non-completion had been issued by the architect.
Durtnell declined to comment on the proceedings and Kaduna was unavailable for comment.
Laverstoke House first hit the headlines as a hidden asset of banknote paper-maker Portals in 1994. This emerged when the firm was taken over by rival printer De La Rue.
In 1995, Laverstoke was sold for £4.25m to former Formula One champion Jody Scheckter.