Visitors usually need at least six months left on their passport from the date they arrive.
Until recently, UK citizens who renewed their passport before it expired could have up to nine months of the remaining validity added to their new travel document.
But the Government has warned this will not count towards the six-month requirement after a no-deal Brexit, meaning people with up to 15 months left on their passport could be denied entry to many popular destinations on the continent.
Now, travellers risk falling foul of rules for entering countries in the Schengen zone such as France, Spain and Italy, according to Which?.
Figures obtained by the consumer group show that around 3.5 million current British passports will not comply with the validity rules.
The consumer group noted that Friday will be three weeks before the UK is due to withdraw from the EU, which is the time it takes for passports to arrive after a standard renewal application.
Rory Boland, editor of Which? Travel magazine, said: “Millions of people could find their holiday plans disrupted or, worse yet, find themselves stranded at the departure gate and prevented from travelling altogether if they fail to renew their passport before the cut-off date.
“Anyone who thinks they might be affected should look to renew their passport today or if you already have travel plans in the near future, consider using the fast-track passport renewal service.”
A Home Office spokesman said: “If there is no deal, new rules would apply when travelling on a British passport to many European countries and some people may need to renew their passport earlier than planned.
“If your passport does not meet the new rules, you should apply for a new passport before travelling to the countries affected.
“You can use the Government’s online passport checker to check a passport for travel to Europe. We recommend that you renew your passport in good time ahead of your travel date.
“In January we launched our ongoing campaign to inform the public of these new rules, and we continue to work with partners in the travel and transport industries to inform people with bookings after March 29.”
“Renew them now”
Daily Star Online previously revealed after Brexit, Brits may need additional deriving permits.
There are three types of International Driving Permits (IDP) which may be required, depending on the country.
A 1926 IDP is needed if driving through Liechtenstein, while a 1949 IDP is needed for Cyprus, Ireland, Iceland, Malta and Spain.
A 1986 IDP would be needed for all other EU countries.