The Anti-Austerity Alliance has criticised the Government for delivering only 20 council houses in the first half of this year and none in the second quarter.
The Department of the Environment described the figures as grossly out of date and predicted that local authorities will have returned almost 5,000 void homes to use over a two-year period ending this Christmas.
The Alliance's Deputy Ruth Coppinger described the most recent official council completion figures as "shameful and shocking.”
She said they expose Government inaction 18 months after its Construction 2020 plan promised what she calls "a measly 449 newly-built council homes" by next March.
She also criticised the less dramatic decline in completions by the much more active not-for-profit sector from 201 in the second half of last year, to 157 in the first half of this year.
But a spokesman for the Department of the Environment described the figures, which are published on its own website, as grossly out of date.
He said local authorities are on course to return 4,800 void homes to use over a two-year period ending this Christmas.
He added that 3,500 social houses are currently under construction and 5,000 units per year will be completed during 2017.
Deputy Coppinger responded that the Department of the Environment had published what it now dismisses as "grossly out-of-date" figures just three weeks ago.
"You now have a situation where the government is contradicting its own figures because they have been highlighted by the opposition," she added in a statement.
And she challenged the government to clarify the situation by publishing up-to-date figures.
Earlier, Ms Coppinger accused the Government of failing to build council houses because of an ideological bias against State investment and its adherence to the EU's fiscal rules which strictly limit new spending on public infrastructure.
She also accused not-for-profit agencies of not being equipped to deal with the housing crisis.