The Channel Tunnel operator said it notched up records for truck and passenger car traffic in the third quarter, despite fears the plunging pound would put Britons off travelling abroad.
However the group confirmed a hit from falling Eurostar demand after recent terrorist attacks, with revenues from its rail network dropping by 5% to 74.1 million euro (£66.3m) in the third quarter.
It said Eurostar carried nearly 289,000 fewer passengers in the three months to the end of September following the terrorist atrocities in Paris and Belgium - a fall of 10%.
Eurotunnel warned in July that the Brexit-hit pound would impact on earnings this year and next.
In its latest update, the group signalled that worries over the fallout from the Brexit vote were overdone.
It said: "There is no sign of slowdown in the UK economy, the FTSE has grown over 10% since the referendum.
"Variations in the value of sterling have had no significant impact on our business in the past and the movement in exchange rates does not damage growth in profitability."
While the plunging pound will mean sales in the UK are worth less when translated into euro, the group said the falls in sterling will help it "significantly" cut its debt repayments.
Jacques Gounon, chairman and chief executive of Eurotunnel, said: "These encouraging signs, combined with new records broken this quarter for the group, put into perspective the change in public opinion following the vote in favour of Brexit: our business has never been stronger."
Eurotunnel said passenger traffic hit a July record of 317,424 cars - beating even the result seen in 1998, when the football World Cup was held in France.
Overall passenger car traffic rose 1% to 2.15 million in the three months to September - its best third-quarter result since 1998 - while the group also saw its highest truck traffic, up 12% at 1.2 million.
It said group-wide revenues lifted 4% to 320.3 million euros (£286m) in the third quarter.
July's profit warning saw Eurotunnel cut its outlook for underlying earnings by 25 million euros (£22.3m) in 2016 and 26 million euros (£23.2m) next year after the pound's drop in value against the euro.
Eurotunnel said that, based on the pound being 7% lower against the euro, its profits were expected to be 4.5% down in 2016 at 535 million euros (£478m), and 4.3% down in 2017 at 579 million euros (£517m).
Eurotunnel saw as much as a third wiped off its stock market value in the immediate aftermath of the Brexit decision, but the stock has since clawed back some of the losses.
Eurotunnel's latest update also showed a return to growth in its cross-channel rail freight arm after a difficult first half caused by the migrant crisis in Calais.
Rail freight slumped 43% in the first six months of 2016, but rose by 11% year-on-year in August and 30% in September.
Eurotunnel faced heavy disruption to its services last summer as migrants at the Jungle camp in Calais made repeated bids to cross to Britain.
The group has spent millions on increased security to help secure the migrant site and new passport controls for people leaving the UK, introduced by the government from April 2015.
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