Jack Dromey, the shadow housing minister, claimed that some of the statistics used were “factually incorrect or deliberately misleading”.
Dromey set out six issues in a letter to Andrew Dilnot, chairman of the UK Statistics Authority.
He said he believed a “casual attitude to accuracy is not only confusing to the public but is obstructing genuine public debate”.
The figures range from the supply of homes to the number of homeless.
Shapps responded by saying Dromey had ignored the Labour government’s “catastrophic” record which saw house building fall to its lowest level since the 1920s.
Dilnot’s predecessor Sir Michael Scholar admitted that the authority was concerned about a “lack of coherence and clarity” in the presentation of housing figures.
Sir Michael replied to a similar letter from Labour MP Nick Raynsford in January, earlier this year.
Sir Michael said: “Looking at statistics on housing, house building and house prices more generally, the Statistics Authority has been concerned for some time that there is a lack of coherence and clarity in their public presentation."
He added: "I recently wrote to the minister for housing proposing that the Statistics Authority should be invited to carry out a formal assessment of the statistics produced by the Homes and Communities Agency and the Tenant Services Authority."
The invitation was not taken up by the Department for Communities and Local Government.
Shapps dismissed what he called Dromey's "incomprehensible rant".
Shapps said: “Not only did his government fail to build more homes, despite the apparent good times, but they actually introduced programmes designed to destroy entire neighbourhoods.
“Their housing market renewal programme bulldozed 10,000 homes, whilst only replacing 1,000. So just to be clear, no one did more to destroy our nation's homes since the Luftwaffe bombs of World War II.”
