Dominic Raab, the housing minister who claimed in an interview last week that immigration had “put house prices up by something like 20%” over the past 25 years, has had to contextualise the figure.

The UK Statistics Authority asked Raab, a leading Brexiter, to publish the evidence for his claim. A document published on Friday by the Ministry of Housing, Communities and Local Government shows that the finding was based on an out-of-date model that had never been intended for this kind of analysis.

Raab defended his use of the model, which estimates the impact of population growth, inflation, interest rates, housing stock and wage growth on house prices.

He said he had been asked specifically about the impact of immigration. “I did indeed say care was needed with the data, and I was right that immigration put average prices up by 20%. We need a balanced approach.”

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The research was conducted using an affordability model described a decade ago in reports by the long-defunct National Housing and Planning Advice Unit. It shows that between 1991 and 2016, the population of England grew from 47.1 million to 54.5 million; the number of non-UK-born residents grew from 3.5 million to 8.4 million over the same period.

But population was one of many factors that had a bearing on house prices. The impact of immigrant households is only a small part of the total. Real income growth, for example, would have pushed up prices by 150%, according to the analysis.

The ministry insisted the information used by Raab was an accurate representation of the research.

Jonathan Portes, a professor of economics and public policy at King’s College London, said it was a reasonable number to try to make a rough estimate, but the evidence on which Raab’s claim was based was so flimsy it could not be described as research.

“The publication is of a standard that I am shocked that [the ministry] would publish. They’ve basically taken an out-of-date model ... it is a very crude back-of-the-envelope approach. It would nonetheless be acceptable to use it for a rough estimate of the impact of an extra 100,000 immigrants next year. What you cannot do is apply that to immigration over 25 years.”

John Healey, Labour’s housing spokesperson, said: “The evidence is clear that immigration is not the major driver of rising housing prices.

“Rather than try to blame others for unaffordable housing costs, Dominic Raab should look at the decisions Conservative ministers have made since 2010. Deep cuts to housing investment have halved the number of new low-cost homes for first-time buyers and driven the number of new social rented homes being built to a record low.”