An MHCLG spokesman also confirmed that the Government would go further, and ban the sale of all new houses sold as leasehold, which was mooted last October.
However, the ban will not apply to retirement homes, or to flats.
The Government has also ditched plans to cap ground rents at £10 a year and reverted to proposals to set it at zero, first announced by Home Secretary Sajid Javid in 2017.
The £10 ground rent cap has been heavily criticised by leasehold campaigners, who said payments at any level would encourage housebuilders to build leasehold homes just to sell them to unscrupulous property investors.
However, banning the sale of new leasehold homes and ending ground rents rely on new laws being passed. With Brexit still undelivered and the ongoing Conservative leadership campaign, there is no little Parliamentary time for these laws to be placed.
Mr Brokenshire said: “We are committed to taking bold action to reform the sector and will be pressing ahead as soon as parliamentary time allows – helping us delivery our promise to make the home buying and selling process quicker, cheaper and easier.”
Sebastian O’Kelly of the Leasehold Knowledge Partnership, the property campaigners, said: “The only dark cloud is that while this is a very welcome move by Mr Brokenshire, it has come at a time of regime change. But it is good news.”