Brexit could lead to a five-fold increase in the number of customs declarations that HMRC must process - from 55 million in 2015 to 255 million, according to the House of Commons Public Accounts Committee.
"The Treasury needs to ensure there is funding in place to develop contingency options so that there are no barriers to continuity of service", it said.
The report warned: 'There are financial as well as operational implications of not acting now.
'Much remains to be done to have an effective Customs Declaration Service in place, on time, and that traders know how to use'. This is a tight timetable at the best of times.
The department has said that CDS is on track and is well governed.
It also urged the Treasury to ensure that funding is in place to develop contingency plans to avoid gaps in the service.
"It 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".
It states: "A failed customs system could therefore 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 report also calls for HMRC to improve its engagement with traders and keep them abreast of the CDS timeline; to "urgently prioritise and make hard decisions" with regard to its "unsustainable" amount of transformation projects; and to report back to the PAC on progress made by March 2018.
Jon Thompson, HMRC chief executive, told the committee last month that the organisation was undertaking a full review of its reform plans to assess how many could be realistically taken forward alongside those relating to Brexit.
"It is clear that there will be many problems if the new customs system is not in place and functioning efficiently by the scheduled date that the United Kingdom is set to leave the European single market and the Customs Union in March 2019".
"Confidence would collapse amid the potentially catastrophic effects", she said, adding that customs should be "banging on the doors of the Treasury" for funding to upgrade the current system.
Committee chair Meg Hillier said the body does not yet have funding to increase the capacity of CDS to deal with the consequences of Brexit - nor to develop contingency options.
'This is deeply worrying.
But Prime Minister Theresa May's spokesman said the customs service was "on track" to be ready in time. We've already allocated over half a billion pounds in funding to ensure a successful exit from the European Union and we will have a fully functioning United Kingdom customs service on day one post Brexit.