Spain and Sweden have confirmed cases of the more contagious coronavirus variant recently identified in the UK, the latest European countries to do so.
The infections were linked to people who had returned from the UK.
France, Denmark, the Netherlands, Italy and Germany, as well as other places outside Europe, have also reported cases in the past few days.
The details given a week ago of the new variant in England triggered travel curbs from dozens of countries.
Scientists say the new variant is considerably more transmissible than previous strains but not necessarily any more dangerous for those infected.
Meanwhile Hungary became the first EU country to start vaccinating people against the disease. The state news agency said the first recipient of the Pfizer-BioNTech vaccine there was a doctor at Del-Pest Central Hospital.
Madrid deputy health chief Antonio Zapatero said the confirmed cases in the Spanish capital involved three relatives of a man who flew from the UK on Thursday.
The fourth case concerned another man, who had also travelled from the UK.
Mr Zapatero said none of the patients were seriously ill and there was “no need for alarm”.
He said there were three further suspected cases of the new variant, though test results will not be ready before Tuesday or Wednesday.
Sweden’s health agency said a traveller there was ill with the strain but had been self-isolating since he returned from the UK.
What do we know about the spread of the new variant?
The new variant first detected in southern England in September is blamed for sharp rises in levels of positive tests in recent weeks in London, south-east England and the east of England
News of the latest cases came just hours after France confirmed its first patient known to have the new variant.
The French health ministry said the person was a French citizen in the central town of Tours who had arrived from London on 19 December.
The ministry said the man, who had been living in the UK, was asymptomatic, and currently self-isolating at home.
France closed its border with the UK after the new variant was confirmed in Britain but ended its ban for EU citizens on Wednesday, providing people tested negative before travelling.
Thousands of lorry drivers spent Christmas Day in their cabs in Kent waiting to cross the English Channel.
Other countries have also reported cases of the new variant: on Friday, Japan confirmed five infections in passengers who had all arrived from the UK, while cases in Denmark, Germany, Italy, the Netherlands and Australia were reported earlier.
Last week, France lifted its national lockdown, but the government said the infection rate had not fallen sufficiently for a further easing.
France has reported more than 2.5 million confirmed Covid infections since the start of the outbreak, with more than 62,000 deaths – the seventh highest total deaths in the world.
The country’s first batch of Pfizer-BioNTech vaccinations meanwhile were delivered from Belgium to the health system’s central pharmacy just outside Paris on Saturday, AFP news agency reports.
The first shots are due to be administered to patients at two facilities for the elderly – in Sevran and Dijon – on Sunday.