An initial deadline for grading countries under a new traffic light system for international travel has been missed.
A report last week by the Commons’ Transport Select Committee said the lists of destinations should be published by Saturday 1 May "at the latest", although this has not happened.
The Department for Transport (DfT) said the lists will be made public in "early May".
Tory MP Huw Merriman, who chairs the Transport Select Committee, said the travel industry has been left "in the dark" and warned the uncertainty "could cost people their jobs".
People in England were previously told the earliest that foreign travel could resume was 17 May, provided the nation meets the government’s four tests for easing lockdown.
These tests include the success of the vaccine programme, reductions in deaths and hospital admissions, low infection rates and a low risk from variants of concern.
Foreign travel will get started again with the new traffic light system to categorise countries based on their COVID risk, and people will still have to take a PCR test after arriving in the UK.
The government is reportedly set to announce next week that traveling abroad will be permitted from 17 May, according to several UK newspapers.
But the Daily Telegraph reports that only a "tiny handful" of countries are expected to be on the "green list" – which requires the lowest level of restrictions.
The majority of European countries are expected to be on the "amber list", meaning people will have to quarantine as well as getting tested.
Ministers plan to review the system at the end of June, before the holiday season begins, which could see vaccinated people able to avoid quarantining.
The hope is that more of Europe will be on the "green list" by this point as many countries impose tougher restrictions to control a third wave of infection.
Greece has said it will invite vaccinated Britons into the country without the need for tests, while Spain, Portugal and France have said they will offer similar in the coming weeks.
The DfT said: "We have always said we will confirm by early May if international travel can resume on 17 May and which countries will fall into which list. This will determine the requirements for travel for passengers.
"The taskforce is working toward restarting international travel in a safe and sustainable way, to allow families and friends to reunite, and businesses to start thriving again, while ensuring we protect public health."