Staff cuts and savings have put the Office for National Statistics under "intense pressure" and could jeopardise the accuracy of its figures, say MPs.
The relocation plans were first raised in 2004
The Treasury Committee said relocating the office to Wales was "inadequately planned and poses risks to the quality of statistics" and should be reviewed.
The MPs said staff were committed but working under an "exceptional burden".
HM Revenue and Customs also relied too heavily on staff cuts to make savings, causing anxiety, the MPs found.
The changes formed part of an efficiency programme following the 2004 Gershon Report.
It called on the departments overseen by the chancellor to save £550m a year, cut 16,850 jobs by 2008 and relocate 5,126 posts out of London by 2010.
But the Treasury Committee urged the Treasury to review the relocation of 850 ONS staff from London to Newport, south Wales, by 2010, saying communication with staff was "haphazard and inadequate".
Its report said: "In the case of the ONS, the organisation is facing a range of pressures.
"Unless action is taken to alleviate some of those pressures, there is a significant risk that the new Statistics Board will inherit an organisation which is unable to perform its tasks to the necessary standard because of structural weaknesses."
It pointed out that ONS statistics are used by the Bank of England in making important decisions - such as fixing interest rates - but the quality of statistics was at risk.
In May the Bank of England also warned that, if lots of skilled ONS staff were unwilling to move to Newport, it could have a "severe impact" on the quality of economic statistics.
The committee urged the Treasury to review the "implementation of the efficiency programme in the ONS or the resources allocated to the department to achieve that implementation"
Both the ONS and HM Revenue and Customs (HMRC) failed to convince MPs of the savings made and quality of services.
The committee said the efficiency drive at HMRC relied too heavily on reductions in the payroll - causing staff much anxiety and potentially risking quality.
And they noted that the two departments were shouldering most of the £550m savings identified - the HMRC on £507m while the ONS had to find £25m. The Treasury had only been asked to find £11.9m savings.
The Tory committee chairman Michael Fallon said both the HMRC and ONS had "failed to convince us that their claims - both on the savings made and the quality of their services - are founded on sufficiently robust grounds."
He said any efficiency programme had to be assessed externally adding: "It is ironic, and a source of concern, that the ONS can't produce statistics on its own performance."
Shadow chief secretary to the Treasury, Philip Hammond, added: "As this report suggests, all too often reductions in headcount are being achieved not by improving efficiency, but by cutting the level of service delivered to the public."