The cross party committee said the number of customs declarations which HM Revenue and Customs must process each year could increase nearly five-fold after Brexit - from 55 million to 255 million.
But HMRC does not yet have the funding to increase the capacity of its new Customs Declaration Service (CDS) to deal with the consequences of Brexit, said the committee.
The department has said using its existing CHIEF system is the main contingency option if CDS isn't ready, something it is developing as a contingency option in parallel with its implementation of CDS.
The report also said there should be a contingency plan in place in case the customs system is not ready before Britain's expected departure in March 2019.
In a report published today, the PAC said HMRC can not use the uncertainty regarding the outcome of Brexit negotiations as an excuse to delay taking action now, and warned of the "catastrophic" consequences of leaving the European Union without a viable system in place.
The report warned: 'There are financial as well as operational implications of not acting now.
Failure to complete a new customs system by the date of Brexit in 2019 will cause massive queues at Dover, a report has warned.
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"HMRC tells us it is merely 'in conversation" over CHIEF upgrade costs when, on behalf of business and the British public, it should be banging on the doors of the Treasury. This is a tight timetable at the best of times.
In 2015, around 55 million custom declarations were made by 141,000 traders. With the hard deadline of Brexit, delay is not an option.
Its report warns that "much remains to be done" to have an effective CDS system in place on time.
It said that HMRC's latest estimate is that 132,000 traders will have to make customs declarations for the first time once the United Kingdom leaves the EU. HMRC, it added, also needs to do a lot more to work with the many businesses affected. HMRC could, for example, update regularly the information it provides to traders on its website which we have been told has not been updated significantly since 2014.
It urged HMRC to ensure that traders are informed of the CDS timeline and progress by January 2018.
It also urged HMRC to ensure that the CDS system and the CHIEF contingency option are capable of managing 255m customs declarations every year, while providing the flexibility to meet the wider challenges of an integrated customs and trade system for the United Kingdom, such as managing changes to tariffs, free trade agreements and worldwide trade quotas.
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