Take-up of the Help to Buy Isa scheme has been lower than expected, according to Government documents.
Detailed Treasury files released alongside the Autumn Statement on Wednesday said take-up had been around half of that assumed in original costings.
Deposit levels were also slightly lower than the limits allowed under the scheme, it said.
Meanwhile, a recent hike in stamp duty for second home buyers, including buy-to-let investors, was now forecast to raise £3.1 billion more than originally expected over coming years.
A three percentage point increase in stamp duty for this sector came into force on April 1 - and estate agents reported seeing investors rush to complete deals before the increase kicked in.
The Treasury's policy costings document said this had been due to raise an expected £3.8 billion from 2016/17 to 2020/21.
But it continued: "Receipts so far have been much higher than expected and we have increased our forecast by £3.1 billion."
Launched last December, Help to Buy Isas offer savers a Government bonus of up to £3,000 to help people save for their first home.
People aiming to get on the property ladder can put up to £200 a month in a dedicated Help to Buy Isa that the Government will top up by 25% - meaning a £50 bonus for every £200 saved.
To get the maximum Government bonus of £3,000, someone will need to have saved £12,000. Homes bought under the scheme can have a purchase price of up to £250,000, or £450,000 in London.
Some commentators have described the accounts as a "no-brainer" for those trying to save up for their first home.
The rates offered by savings providers have compared well with the Isa market generally - although some of these rates have been cut in the low interest rate environment.
The Treasury documents said of the Help to Buy Isa: "We originally expected this to cost £2.1 billion from 2016/17 to 2019/20.
"Take-up has been lower than expected, around half that assumed in the original costing, with deposit levels also slightly lower than the allowable limits under the scheme.
"This reduces the expected cost to £1.2 billion from 2016/17 to 2019/20. Uncertainty remains around these assumptions."
Separate figures released by the British Bankers' Association (BBA) showed the number of mortgages being handed out in October to home buyers was down by 10% compared with October 2015.
Despite being lower than a year earlier, the lending figure was still the highest in five months.
Economists said the BBA's figures suggested that recent cuts in mortgage rates, following the chop in the Bank of England base rate to 0.25%, had only led to a modest uplift in mortgage borrowing.