Britain was scrambling to draw up mass evacuation plans to bring home more than 100,000 citizens stranded in Middle East countries under attack from Iran.
Foreign Secretary Yvette said the Government was working on “every possible option” to rescue Brits stranded in the war zone.
British rapid response teams are being sent to Gulf states and other countries to work with the travel industry on plans to get Britons home.
Ms Cooper said there were 300,000 British citizens in states being attacked by Iran including Dubai, Abu Dhabi, Kuwait and Bahrain.
Just over 100,000 Britons had registered their presence with the Foreign Office.
A majority of the Britons are holidaymakers, were transiting through hub airports in the region, or are business people, rather than having a permanent home in the country where they are now.
Some of them had been in hotels hit by Iranian attacks, either directly or by debris.
“There may be many more people we would want to register,” Ms Cooper said.
“At the moment in most of those countries the advice is to shelter in place,” she added, with airspace closed in many areas.
But she said it was a “rapidly evolving situation”.
British Foreign Office teams are working with transport industries in Gulf countries on how to get Britons out of the war zone if it is possible to do so by commercial flights.
However, the evacuation plans are also being drawn up, with reports that it could be through Saudi Arabia, if the situation deteriorates rapidly.
Consular teams are already offering additional support to Britons such as ensuring they can get medicines they need if they are running out.
Ms Cooper said that Britain had allowed the US to use British military bases to launch “defensive action” strikes against Iranian missile and drone sites after the Tehran regime attacked countries not involved in the initial US air strikes to topple the Iranian regime.
British military personnel at a base in Bahrain narrowly avoided being hit in an Iranian strike.
The Foreign Secretary highlighted missile launchers in southern Iran which were targeted towards Gulf countries.
She also confirmed that the runway at the RAF Akrotiri base in Cyprus had been hit by a drone.
Ms Cooper told Sky News: “This is about the defence of our partners in the Gulf and defence of countries where we have so many British citizens and interests in those those countries.
“We continue to believe that we want to seek negotiated solution, a diplomatic process.
“That’s always been our view and it’s one of the reasons why we made a deliberate decision not to be involved or provide support for the US strikes that took place over the weekend.”
She went on: “It’s a specific, limited agreement about the defence of Gulf countries, and many of those Gulf countries were not involved in any of the strikes on Iran.”
Iran unleashed a wave of dawn attacks across the Middle East with several warplane being shot down over Kuwait.
Explosions were reported in Bahrain, at or close to a US naval base, and smoke was seen rising near the US embassy in Kuwait.
Unconfirmed reports and photos showed a US pilot being rescued after apparently ejecting over Kuwait.
There were claims that his F-15 plane had been accidentally shot down.
There were also reports of explosions in Dubai and Abu Dhabi.
US consular chiefs told American citizens in Kuwait to take cover.
“There is a continuing threat of missile and UAV attacks over Kuwait. Do not come to the Embassy.
“Take cover in your residence on the lowest available floor and away from windows.
“Do not go outside.”
