A report issued by the committee today states: "A failed customs system could lead to huge disruption for businesses, with delays potentially causing massive queues at Dover and resulting in food being left to rot in trucks at the border".
The PAC said, "The existing CHIEF system is its main contingency option, but we are surprised to hear that HMRC and HM Treasury (HMT) are still only "in Brexit and the future of Customs conversation" over the £7.3m needed to upgrade CHIEF".
The parliamentarians estimated that the number of declarations that customs must process each year could increase from 55 million to 255 million.
A government spokesperson said: "The Customs Declaration Service is on track for delivery by January 2019 and has the capacity to deal with a significant increase in customs declarations at the border".
"Much remains to be done to have an effective Customs Declaration Service (CDS) in place, on time, and that traders know how to use", MPs from the House of Commons public accounts committee said in a report.
"HMRC is under considerable pressure to deliver the new Customs Declaration Service (CDS) in time, but it does not yet have funding to increase the capacity of CDS to deal with the consequences of Brexit - nor to develop contingency options".
"Failure to have a viable customs system in place before the UK's planned exit from the European Union would wreak havoc for United Kingdom business, trade and our worldwide reputation".
"This is deeply worrying". HMRC requires a relatively small sum to upgrade the current Chief (Customs Handling of Import and Export Freight) system - a move which would provide some peace of mind to traders, many of whom are still operating with limited information and in great uncertainty.
"It (HMRC) needs to progress this work urgently and obtain the additional funding required, to ensure that CDS can deal with the potential increase in volumes, and that an adequate fall-back option is in place in case this is delayed".
The report described the introduction of CDS as "a programme of national importance that could have a huge reputational impact for the United Kingdom if it is not delivered successfully". This is a tight timetable at the best of times.
"In 2015, around 55m customs declarations were made by 141,000 traders".
'The Treasury needs to ensure there is funding in place to develop contingency options so that there are no barriers to continuity of service.
HMRC boss John Thompson warned MPs last month that he would need significantly more staff if Britain was to cope properly with a collapse in negotiations with Brussels over trade deals.