He claims, that after the builders left, he had to replace windows, finish off a driveway, redecorate inside and out, finish boundary walls, install gates, resand and reseal floors and put right bathroom fittings.
The writ adds that Galvin also repaired part of the garden and carried out remedial works.
Galvin had employed the company, of Evesham, Worcestershire, to carry out renovation and refurbishment to his property in Greencroft Gardens.
The writ says: "Avondale supplied budget costings for the work, but the company's fees were higher than reasonable, and higher than the budget costing."
The writ adds that his agreement with the building company contained an implied term that Galvin would pay a reasonable fee for the work, or that the fee would not exceed the budget costings supplied by the company.
Galvin, who has been dubbed the "King of Colour" and whose awards include World Hair Colourist of the Year, now claims that the company breached its obligation to use reasonable skill and care in carrying out the project and failed to finish the work.
Avondale developments refused to comment but it is understood that it intends to begin legal procedings over the matter itself. Galvin was unavailable.
A date for the High Court hearing has not been set.
Infinite alleges that Canary Wharf has declined to pay for the work but has failed to issue withholding notices.
Infinite is providing plasterboard partitions and suspended ceilings for the project, called HQ2. Infinite applied for an interim payment of £1,599,000 on 19 September this year and then revised this figure to £1,730,000.