“Max fac”, which stands for maximum facilitation, relies on technology and trusted trader schemes to minimise customs checks.
Earlier this year research predicted that each customs declaration could cost between £20 and £55, however ministers later advised this may be closer to £32.50.
The system was addressed by HMRC chief executive Jon Thompson at a Treasure Select Committee hearing and is being supported by Brexiteers such as Boris Johnson, Liam Fox, Michael Gove and Jacob Rees-Mogg.
Thompson suggested prime minister Theresa May's preferred option of a "customs partnership", which would collect tariffs set by the EU on goods coming into the UK, would ultimately be cost neutral after £700m in set-up costs if tariffs were reclaimed by businesses.
Nicky Morgan, chair of the Treasury committee, summarised the session by saying that there will be a “functioning but sub-optimal border” on January 2021 where a “trade off between friction, revenue and security” would occur.
Whatever deal the government choses to go for, it will take between three to five years to get the new arrangements in place.
She said HMRC is recruiting about 5,000 people to make this happen, leaving aside people at the border, and is spending £260m implementing Brexit.
“There are 39 other HMRC projects which have either had to be stopped or significantly slowed down in order to get Brexit through,” Morgan added.
She asked Thompson, “Wouldn’t it be a relief if parliament just voted for a customs union?” He replied that was for the Parliament to decide.
A Number 10 spokesperson told the Telegraph that the £20bn figure was “speculation”.
Paul Blomfield, shadow Brexit minister, said, “This latest warning underlines that the sensible option, and the only way to protect jobs and our manufacturing industry, is to negotiate a new customs union with the EU.
“Rather than pursuing policies that will cost British businesses billions, the government should follow Labour’s lead and back a new comprehensive customs union,” he added.
Britain’s biggest business lobby group, the Confederation of British Industry urged earlier this year for a comprehensive customs union after Brexit, and warned that both the UK and the EU could not afford higher barriers.