He noted that this method would effectively introduce a cap of £2,500 on the total bonus that any individual could receive in one year, and provide a total annual incentivised savings capacity of £8,000 plus £2,500 in bonuses, "more than enough for almost everyone".
Mr Johnson said: "This approach would be to particularly encourage the most reluctant savers, including those who may find it hardest to save anything at all."
An HM Treasury spokesperson said: "We want people to save into a pension, which is why we offer tax relief on the contributions made.
"This new data gives us a more accurate picture of how the relief is working and shows that pensioners are receiving more payments from their private pension savings than previously estimated.
"The full cost of pensions tax and national insurance contributions relief, £54bn, has not changed."
Ricky Chan, director and chartered financial planner at London-based IFS Wealth & Pensions, agrees with Sir Steve.
He said: "Such large deviations from the actual and estimated figures, for both the income tax receipts and tax relief, should prompt the government to review whether their policy towards pensions is actually working to give long-term benefits to society (rather than simply fill up the government’s coffers).
"Of course the policies were designed to raise tax receipts, but is this creating previously unforeseen issues to society?"