Jimmy Whitworth, professor of international public health at the London School of Hygiene and Tropical Medicine, said the risk to people in the UK remains "very low", but travellers abroad, including pregnant women, should take precautions.
He said: "Summer is approaching fast and the risk of Zika spreading to Europe is real.
"The main mosquito vector for Zika, Aedes aegypti, is only found in Madeira and around the Black Sea, but another mosquito, Aedes albopictus, is more widespread and is capable of transmitting Zika, although not very efficiently.
"It is possible that Zika virus could be introduced into European Aedes albopictus and cause outbreaks this summer or in future years."
Prof Whitworth said the mosquitoes that spread Zika are not found naturally in the UK because the climate is too cold, even in summer, and there is virtually "no chance" of an epidemic in the UK.
But he added: "Countries in Southern Europe, including France and Italy, need to be especially vigilant, and it's important that holidaymakers follow public health advice while abroad, including taking all the necessary precautions to avoid getting bitten.
"This is especially so for pregnant women, or women planning to become pregnant, travelling to areas where there is Zika, as there is now a proven link with microcephaly and other birth defects."
Prof Whitworth also said a UK-wide contingency plan for invasive mosquito control should be developed.
Paul Hunter, professor of health protection at the University of East Anglia, agreed: "The World Health Organisation warning about the risk of Zika virus in Europe is timely and real.
"There have already been indigenous European outbreaks of two closely-related viruses - Dengue and Chikungunya - that are spread by the same mosquito."
He said any European outbreak "would be relatively short-lived".
"Nevertheless an outbreak occurring in the Mediterranean area could still have repercussions throughout Europe if pregnant holidaymakers acquire the infection, or if males then pass the infection sexually to their pregnant partners.
"If and when the disease does come to Europe, it will be essential that people are very careful about using insect repellents and use condoms during sex if they think they have been exposed."