The more contagious coronavirus strain has been reported in at least seven nations around the world.
Germany, Australia, France, Denmark, the Netherlands, Italy, Spain and Japan have reported cases.
Spain confirmed four cases of the UK strain, all in Madrid and linked to recent travel, deputy health chief said.
Madrid deputy health chief Antonio Zapatero said the confirmed cases 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.
France has also 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.
The new coronavirus variant in England was first found in September and is being blamed for sharp rises in levels of positive tests in recent weeks in London, south-east England and the east of England
The news of the new strain panicked nations around the world – about 40, forcing many to impose travel curbs on the United Kingdom.
Scientists say the new variant is considerably 70 percent more transmissible than previous strains but not necessarily any more dangerous for those infected.
The new variant is massively replacing the other versions of the virus and its mutation shown in the lab increase the ability of the virus to infect cells faster – meaning spread more easily.
However, experts are positive about the vaccine developed by Pfizer and BioNTech working on the new variant of the virus.