The FCO also said it was "working to find out if any more need our help" and that the numbers of those injured could rise, BBC News reports.
Police said five suspects killed in the Spanish resort town of Cambrils, near Salou, were carrying bomb belts and had run over civilians with a car, Sky News reports.
A woman has now been confirmed to have died following the incident, which saw attackers plough into people - including a police officer - in an Audi A3.
It came just hours after a van drove into crowds of people in Las Ramblas, Barcelona, killing 13 people and leaving at least 100 injured.
The Catalan government has confirmed the two attacks were linked, Sky News reports.
So-called Islamic State said it was responsible for the Barcelona attack, in a statement through its propaganda agency Amaq.
The suspects in Cambrils were carrying explosive belts and a bomb squad carried out several controlled explosions, police said.
The FCO said on its website that the British Embassy in Madrid and Consulate General in Barcelona were in contact with local authorities and “urgently seeking further information” following incidents.
It advises those in the immediate area to “take care and follow the advice of the local security authorities”.
It said: “If you’re caught up in an ongoing incident, turn any mobile phones or other devices to silent, and do not put your location on social media.
“Follow the advice of the local authorities when instructed. If you are safe, follow the instructions of the Spanish authorities and notify friends and family via social networks, to avoid using phone lines.”
A helpline has been set up on 0034 93 214 21 24.
Some public transport, particularly the metro, has been affected.
Abta has advised travellers in the region to "remain alert and vigilant" and allow for extra time for their journeys in case of disruption.
The association added: "People imminently due to travel to Barcelona or Costa Dorada should monitor FCO advice and check the status of their flight with their airline or travel provider.
"We are not aware of any disruption to flight services as a result of these incidents.”
