Ministers were critical of the warning given at a Select Committee with HMRC bosses refusing to guarantee everything would be ready by the March 2019 Brexit deadline.
If the UK ditches the EU customs union in a Hard Brexit scenario would see customs declaration increase fivefold from 50million to 250million.
To try and deal with this increase, without causing delays, plans are already underway to hire and train 5,000 new Border Force staff.
A new Customs Declaration Services (CDS) computer system will also be introduced by the end of 2018 aimed at speeding things up.
This will need to be complemented by new lorry parks and checkpoints, the HMRC have claimed.
Ministers have claimed the five-year estimate is overly pessimistic.
A government source said to The Sun: “The main thing HMRC need is CDS, which will be in place from October 2018.
“It’s possible there may be longer term ‘nice to have’ things that could take around that time scale, but they are not business critical to a successful Brexit.”
In a separate warning, HMRC officials have told ministers delays of even a few minutes could cause tail backs of a similar those seen during Operation Stack in 2015.
With “no deal” looking like an increasingly likely outcome from talks Theresa May’s cabinet are set to discuss preparations for crashing out of the European Union in their weekly meeting today.
Downing Street said “all contingencies” will be discussed by cabinet members in the regular Number 10 session.
That will include what happens if there is no deal, alongside the PM’s hopes for progress on a trade agreement.
It comes amid mounting pressure from her own party to prepare for the prospect of failing to reach an acceptable agreement with Brussels.
Brexit Secretary David Davis, who has spent months negotiating with Brussels as progress stalled, is expected to lead the discussions.