Leaving the European Union’s trading arrangements offers the chance to “transform our country”, Boris Johnson claimed as UK businesses adjusted to the new bureaucracy.

There was little sign of disruption at the border as freight travelled to France and Ireland on a quiet bank holiday after the new arrangements came in at 11pm on New Year’s Eve.

The Prime Minister said leaving the single market and customs union meant the UK has “taken back control of our money, our laws and our waters”.

Lower trade volumes on the New Year’s Day bank holiday meant there was little disruption from the additional red tape that now applies on exports to the EU.

Eurotunnel spokesman John Keefe said on Friday that services are running “very, very smoothly”.

He told the PA news agency: “There’s very little change and it doesn’t add any time, which is the crucial piece of it.”

Four truck drivers were turned away but all as a result of failing to produce coronavirus test certificates, rather than falling foul of new customs rules.

The Port of Dover told PA that “everything is running smoothly”.

It was a view echoed in Calais on the other side of the Channel but the region’s customs director Jean Marc Thillier warned the arrangements would face a “trial by fire” when traffic flows increase after the holiday weekend.

Mr Johnson said the decision to leave the single market and customs union ended a “47-year experiment” of European Union membership.

The EU had provided the UK with a “safe European home” during the 1970s, but the country has now “changed out of all recognition” with global perspectives, he said.

Mr Johnson, writing in the Daily Telegraph, said the “great new deal” with the EU secured on Christmas Eve honours the “most basic promises” of the 2016 referendum and meant the UK has “taken back control of our money, our laws and our waters”.

In a sign that the UK will break away from the EU rules it inherited, Mr Johnson said: “We need the Brexit-given chance to turbocharge those sectors in which we excel, to do things differently and to do them better.”

Ireland’s foreign minister, Simon Coveney, said the change in trading arrangements with the UK will inevitably cause disruption.

He told BBC Radio 4’s Today programme: “We’re now going to see the 80 billion euro (£71.2 billion) worth of trade across the Irish Sea between Britain and Ireland disrupted by an awful lot more checks and declarations, and bureaucracy and paperwork, and cost and delay.”

Ferry operator Stena Line said six freight loads destined for Ireland had been turned away at Holyhead due to incorrect paperwork.

Former minister David Jones, deputy chairman of the European Research Group (ERG) of Brexiteer Tories, said “a border in the Irish Sea was something that we did not expect, nor did we approve of”.

He told the BBC that while “it does amount to a barrier” the UK Government had “done a great deal to mitigate the problem, but I think it is going to take some time before the new arrangements bed in”.

The Northern Ireland Protocol means Northern Ireland remains in the EU single market for goods and will apply EU customs rules at its ports, even though the region is still part of the UK customs territory.

The protocol will also see Northern Ireland follow certain EU rules on state aid and VAT.

In other developments:

– Nicola Sturgeon said the EU should be ready to welcome an independent Scotland back into the bloc. The First Minister said: “Scotland will be back soon, Europe. Keep the light on.”

– French president Emmanuel Macron used his new year’s message to say that while the UK remains a “friend and ally”, Brexit was born of a European malaise and “many lies and false promises”.

– Chancellor Rishi Sunak abolished the “Tampon tax”, removing VAT on sanitary products, something which was not possible under EU rules.

Under the new arrangements, freedom of movement rights end and, while UK citizens can still travel for work or pleasure, there are different rules.

Passports must be valid for more than six months, visas or permits may be needed for long stays while pets need a health certificate.

The automatic right to live and work in the EU also ceases, and the UK will no longer take part in the Erasmus student exchange programme.

Hauliers face new rules and lorry drivers heading for the Continent must have a Kent Access Permit before entering the county in an effort to curb tailbacks on cross-Channel routes.

Gibraltar, whose sovereignty is disputed by Spain and Britain, remains subject to the rules of the free-travel Schengen area, keeping the border with Spain open.

Big Ben chimed at 11pm on New Year’s Eve, when the Prime Minister is understood to have marked the occasion with his family in Downing Street.

Brexit Party leader Nigel Farage, who played a key role in the 2016 referendum, told PA: “Yes, we spare a thought for Northern Ireland and our fishermen, but this is a moment to celebrate 2021 as an independent United Kingdom.

“It’s a shame the pubs aren’t open.”