The group's bunkering subsidiaries Lanka Maritime Services and Lanka Bunkering Services are parties to the action.
Nanayakkara has filed a fundamental rights case demanding the cancellation of the sale of LMS to John Keells Holdings (JKH) in 2002.
He alleged that the sale of prime land near Colombo port with LMS bunker storage tanks had been done fraudulently and that the effective monopoly given to LMS after privatization was also fraudulent.
JKH profited from the LMS bunker supplier's effective monopoly for several years before it was successfully challenged by the Sri Lanka Shipping subsidiaries in the Appeal Court.
The Attorney General subsequently ruled that other firms with bunkering licences could also sell bunkers to ships in Colombo.
Sri Lanka Shipping, an unsuccessful bidder short-listed for the 90 percent stake in Lanka Marine Services, said in its statement on the court intervention that it was "directly affected" by the alleged irregularity or illegality in the privatization.
In the affidavit filed by Mohamed Reza, Managing Director of Sri Lanka Shipping Group of Companies, the firm states that they have been shocked, dismayed and alarmed by the serious allegations contained in the main petition.
This includes the allegation that John Keells Holdings was granted far-reaching and iniquitous favours, concessions or advantages in the LMS sale, without the knowledge or approval of the Cabinet of Ministers or the other bidders, the affidavit said.
Sri Lanka Shipping said it had been assured during the bidding stage that LMS would not retain a monopoly on the import and sale of bunkers after it was privatized.Reza in the affidavit also said that the company believes the LMS privatization was fraudulent and not done in a transparent and equitable manner.