Earlier this year officials admitted they had discovered 40,000 case files – some dating back to the 1980s – where there was no record of whether the individual had left the country.
The stark message risked reopening the row between the Home Office and the Office for National Statistics (ONS), whose projections say the landmark total will be hit within two decades.
However, Mr Johnson insisted the country “would cope” if the population did hit such a level but predicted again that it would not happen.
He was speaking ahead of a public debate on immigration between himself, his Tory shadow Chris Grayling and Liberal Democrat home affairs spokesman Chris Huhne, believed to be the first of its kind.
It comes after The Daily Telegraph told that more than one in ten of the UK population was born abroad after hitting record levels.
Official figures published by the ONS say the total UK population will increase by nearly nine million to hit 70 million by 2028.
A similar projection was repeated yesterday by Jil Matheson, the national statistician, who said numbers will hit 71.6 million by 2033 on current trends.
The Home Office and ONS were embroiled in a major row in March this year after Phil Woolas, the immigration minister, accused the statistics body of a “sinister” release of immigration data.
He claimed the ONS was “playing politics” over the way if released some information, which came at a time concern over the influx of foreign workers was at a peak.