At least 359 people were killed in the attacks last weekend, including eight Britons.
An estimated 8,000 British holidaymakers are in Sri Lanka. In addition there are up to 10,000 UK citizens who are long-term residents.
The last major tourist nation to be placed on the no-go list was Tunisia, following two terrorist attacks in March and June 2015.
On that occasion, and after the ban on flights to Sharm el Sheikh in November 2015, an airlift was organised by travel firms.
But The Independent understands that British tourists and their travel companies will be left to make their own arrangements.
There is only one direct flight a day from Colombo to the UK – the Sri Lankan Airlines departure to Heathrow.
Many British travellers fly on Emirates and Qatar Airways, but flights from Colombo are extremely busy as visitors of many nationalities try to leave Sri Lanka.
Those who were booked to return at the weekend, for example, will be expected to travel back as planned.
The new travel advice invalidates the travel insurance of any UK traveller who decides to ignore the warning by not leaving in a timely fashion.
The foreign secretary Jeremy Hunt said: “Our hope is that it will be possible to change this when the current security operation has concluded.”
The Tunisia ban was lifted after two years.
Abta, the travel association, said in a statement: “Customers who are due to travel imminently to the island on package holidays will be offered options of deferring their date of travel, transferring to another destination or a full refund.
“Customers who have booked independently will need to discuss their options with their airline and accommodation provider.”