The Public Accounts Committee warned of "huge disruption" to businesses, "massive queues" at Dover port and food rotting in lorries at the border.
"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 global reputation".
The government said the project was on track to be delivered in January 2019.
Under Theresa May's plan for Brexit, the United Kingdom will leave the single market and the customs union.
Ms Hillier said HMRC was under "considerable pressure" and did not have the funding to develop customs systems for Brexit or plan contingencies.
"This report makes for stark reading for businesses and consumers who are dependent on moving goods quickly between the United Kingdom and the rest of Europe".
At this point, depending on the nature of the goods, taxes and duties may be payable.
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.
Failure to complete a new customs system by the date of Brexit in 2019 will cause massive queues at Dover, a report has warned.
"This is a programme of national importance that could have a huge reputational impact for the United Kingdom if it is not delivered successfully".
The committee said HMRC should begin talking to traders immediately, rather than waiting until a new arrangement was agreed. As part of its plans to broaden engagement with traders, it should also promote the benefits of obtaining trusted trader status and aim to increase the number of registered traders, the PAC said.
The committee also warned that HMRC was now managing an "unsustainable" number of reform projects, which could risk the delivery of the CDS system, saying it urgently needed to "prioritise and make hard decisions". "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 UK can not afford for this to go wrong".
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 global trade quotas.
The government has said it will hire an extra 5,000 customs staff to cope with Brexit.
During the transition between the two systems, the old version would operate in tandem with the new one, he added.
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