The firm submitted the statement of claim in the confidential arbitration process to settle its dispute with German developer TrizecHahn.
The scheme was finished last year.
Laing had been expected to ask for £20m, but the 200-page statement of claim explains in detail why it believes it is owed more than £28m.
Laing declined to comment, but a legal source who has seen the statement of claim said it hinged on two points.
The first is that Laing was delayed for a year by an archaeological dig next to the Bank of England. During this time, the contractor says it ran up huge expenses extending its programme of work.
Its second key argument is that it was not compensated for the cost of “developments” it made to the design during construction.
These were carried out and the client was billed, but they were rejected as an extra cost.
The design-and-build contract had a £33m guaranteed maximum price, but Laing argues that changes in the scope of its work mean it should be paid extra.
TrizecHahn has about six months to prepare a defence to Laing’s claim.
It is expected to argue that the GMP should be the maximum it pays, in a case seen by many lawyers as a test of GMP contracts.
Legal sources said there was a chance the dispute would be settled, but Laing is understood to be digging its heels in over the case, and is unlikely to settle for less than £20m.
The Stirling Wilford-designed office project was fraught with difficulties, eventually finishing 18 months late.
Laing had payment difficulties throughout, and at one stage considered pulling out, before deciding that this would leave it open to criticism from TrizecHahn.
The German developer, which was client for the project in partnership with site owner Lord Palumbo, is claiming up to £10m from Laing for its own delay costs. It declined to comment this week.
If the case reaches the full arbitration process, private hearings are likely to be held in summer 2000.
Laing won the project at the height of the early 1990s recession, and there was speculation at the time that it had under-bid for the job.
Other contractors, including Bovis, that bid for No 1 Poultry submitted far higher bids, but Laing was insistent that the scheme could be built for £33m.