Britons are being warned to prepare for “some disruption” when the UK leaves the EU on January 1.
According to cabinet minister Michael Gove, there will be “practical and procedural changes” despite the country agreeing a free trade and security deal with the bloc.
Mr Gove told the BBC the UK had "a fantastic free trade agreement", but said with "big change" comes "challenge and opportunity".
Brits travelling to the EU from the UK are currently exempt from paying mobile phone roaming charges and can access free healthcare using a European Health Insurance Card.
But the Brexit agreement, which will be voted on by MPs on Wednesday, does not include these advantages - and will end on New Year's Day.
Businesses that trade with the European Union are being urged to make sure they have the right documentation in place to avoid extra costs and delays after Brexit.
After January 1, companies will need to complete customs declaration forms to export and import goods from the bloc - even though a deal has been secured.
Businesses will also need an EORI number to move goods between the UK and the EU. If companies do not have an EORI they may also face increased costs and delays.
"The nature of our new relationship with the EU - outside the single market and customs union - means that there are practical and procedural changes that businesses and citizens need to get ready for, and time to make these final preparations is very short," Mr Gove told the BBC.
"We know that there will be some disruption as we adjust to new ways of doing business with the EU, so it is vital that we all take the necessary action now."
The deal is the biggest bilateral trade deal signed by either side, covering trade worth £668billion.
