Passengers arriving at Manchester Airport, on a flight from Cancun in Mexico
The government is advising that people go to Mexico only if their travel is "essential".
And tour operators have started to cancel imminent holidays and flights.
What will happen if you chose to cancel your trip, or if it is cancelled for you?
My holiday company has just cancelled my trip - can I get my money back?
You should be able to chose a new holiday with the tour operator, or ask for a refund.
Firstly, you should be offered "suitable alternative arrangements" by the company, says the travel association ABTA.
If that cannot be done, then a full refund will be due of the money you paid the operator.
But you will not be compensated for any inconvenience.
I want to follow the government's advice - can I just cancel my flight and get my money back?
If you cancel and have travel insurance you may be able to recover the cost of the lost flight booking, says the Association of British Insurers (ABI).
"Travel insurance will normally cover the cost of cancelling a trip for a number of specified reasons, including illness, and redundancy," says the ABI.
"If the government advises against travelling to a particular country or region, check your travel policy, as some may cover cancellation costs, although policies vary."
Are British Airways still flying?
Yes, they have four flights a week to Mexico City and they are still flying them.
BA says it will let worried passengers defer their bookings to a later date, or fly them somewhere else instead, if they do not want to go.
The same goes for a combined flight and hotel deal.
If BA took the decision to cancel its flights, then a full refund would be payable to passengers.
At this moment BA is not offering a refund to anyone who just wishes to cancel their bookings altogether, but they are keeping this point under review.
What if I insist on going, despite the government's advice?
If you do so this may invalidate a travel or health insurance policy which may well state that you should obey government travel warnings.
I paid for my holiday by credit card - is that relevant?
Yes. If you paid more than £100 then the card company becomes equally responsible for refunding you if your flight or hotel are cancelled.