The firm's appointment was announced in a House of Commons written answer last week.
It follows revelations in Building (29 January) of the cost breakdown of Portcullis House, which was designed by Sir Michael Hopkins & Partners and is now being built by Laing.
MP for Roxburgh and Berwickshire Archie Kirkwood, representing the House of Commons Commission said: "The commission has authorised a mid-term review of progress on Portcullis House.
"The objective of the review, which is part of a continuing programme of supervision on the project, will be to satisfy the commission that the parliamentary building can be delivered to the desired quality, on budget and within the agreed timetable.
"The honorary lady [Baroness Dean put down the question] will be aware that in approving the principle of the new building, the house itself was well aware of the important heritage implications of what will be a major parliamentary development on an internationally important site.
"While the commission recognises that Portcullis House needs to be a building of the first architectural quality, it has also been concerned throughout with the need to keep costs in control.
"The review, to be conducted by Northcroft, will analyse cost movements to date and include an independent risk appraisal of out-turn costs. It will also provide an opportunity to examine organisational structure and procedures used during the project."