Up to 15 people were killed after Israeli commandoes boarded ships carrying 10,000 tonnes of aid en route from Cyprus.
William Hague said the British embassy was in "urgent contact" with the Israeli government, asking for more information.
He said: "I deplore the loss of life during the interception of the Gaza flotilla. Our embassy is in urgent contact with the Israeli government.
"We are asking for more information and urgent access to any UK nationals involved.
"We have consistently advised against attempting to access Gaza in this way because of the risks involved. But at the same time, there is a clear need for Israel to act with restraint and in line with international obligations.
"It would be important to establish the facts about this incident and especially whether enough was done to prevent death and injuries.
"This news underlines the need to lift the restrictions on access to Gaza in line with UNSCR (UN Security Council Resolution) 1860."
Mr Hague continued: "The closure (of access to Gaza) is unacceptable and counter-productive. There can be no better response from the international community to this tragedy than to achieve urgently a durable resolution to the Gaza crisis.
"I call on the Government of Israel to open the crossings to allow unfettered access for aid to Gaza, and address the serious concerns about the deterioration in the humanitarian and economic situation and about the effect on a generation of young Palestinians."
Mr Hague's criticism of the killings comes after several groups condemned the action taken by the Israelis.
Among those travelling on the flotilla of six were eight Irish citizens.
Michael Martin, Irish Foreign Affairs Minister, said: "The reports of up to 15 people killed and 50 injured, if confirmed, would constitute a totally unacceptable response by the Israeli military to what was a humanitarian mission attempting to deliver much needed supplies to the people of Gaza."
Palestinian rights group Friends of Al-Aqsa said that 28 British citizens were travelling on the ships, including its chairman Ismail Patel.
There has been no communication from him since the inexcusable attack, it said.
The Stop The War Coalition (STWC) said the action "should see Israel condemned under international law".
The boats were taking aid to an Israeli blockade set up three years ago after Hamas militants seized power there.
Greta Berlin, spokeswoman for the Free Gaza movement, which co-ordinated the flotilla said: "It's disgusting that they have come on board and attacked civilians. We are civilians."
Israeli military spokeswoman Lt. Col. Avital Leibovitch said: "They planned this attack. Our soldiers were injured from these knives and sharp metal objects ... as well as from live fire." Two of the dead activists had fired at soldiers with pistols, the army added.
The Turkish Mavi Marmara ship, from the pro-Islamic aid group IHH, and Free Gaza's Challenger 1 are understood to have been boarded by Israeli Navy ships in international waters, 80 miles off the coast of Gaza.
Dr Fintan Lane, Fiachra O Luain and Shane Dillon, all from Ireland, were on Challenger 1 which had travelled from Cyprus in the first wave of the flotilla.
The Ireland Palestine Solidarity Campaign (IPSC) said it has not been able to contact any of its members on the ships.
Dr David Landy, IPSC chairman, also accused Israel of breaching international law.
Dr Landy claimed: "The fact that Israel would allow its forces to kill and wound international human rights activists shows the world once again that Israeli is a rogue state that acts with impunity."
Internet footage has emerged showing pandemonium on board the Mavi Marmara, with activists in orange lifejackets running around as others tried to help a colleague lying on the deck.
A spokesman for the Israeli embassy in London said today: "We have no doubt regarding the real intention of the flotilla. It's not about humanitarian aid.
"You can see clearly from the footage that when they boarded they were attacked with knives and sharp metal objects and left with not much option but to respond.
"There was no intention whatsoever to use any of the weapons soldiers naturally carry. As soon as the soldiers boarded they were attacked by knives and life-threatening objects.
"In the first few seconds the soldiers tried to protect themselves with their hands and avoid using the guns."
The flotilla left the coast of Cyprus yesterday afternoon. Three Israeli navy missile boats are understood to have mobilised after dark to challenge it.
The boats were carrying building materials, crayons, chocolate for children, medical supplies including a CT scanner, a complete dental surgery, and paper for schools, the Palestine Solidarity Campaign said.
Pictures of activists with sticks bludgeoning an Israeli soldier as he tried to land on a boat from a helicopter were shown by Turkish channel NTV.
Satellite news channel al-Jazeera reported from the lead Turkish ship saying Israeli forces fired and boarded, leaving its captain wounded.
Nobel peace prize winner Mairead Maguire was on board the Irish ship MV Rachel Corrie which left in the second wave of the flotilla.
Holocaust survivor Hedy Epstein, 85, and several EU MPs are also believed to have been part of the flotilla.
The Turkish Foreign Ministry condemned the interception and said it was summoning the Israeli ambassador.
The Israeli army said four soldiers were wounded, including one hit by live fire.
Mark Regev, a spokesman for Israeli Prime Minister Benjamin Netanyahu, who is in Canada, said: ""We did not want to see confrontation.
"We made repeated offers to the boats that they come to the (Israeli) port of Ashdod unload the humanitarian cargo, and we guaranteed to pass all humanitarian items through the crossings to the Gaza Strip. Unfortunately, they rejected our offers and chose the path of confrontation."
The head of the Gaza Hamas government, Ismail Haniyeh called the attack "brutal".
Former Prime Minister Tony Blair, who is the Quartet Representative in the Middle East, said: "I express deep regret and shock at the tragic loss of life.
"There obviously has to be a full investigation into what has happened.
"Once again I repeat my view that we need a different and better way of helping the people of Gaza and avoiding the hardship and tragedy that is inherent in the present situation."
Islington North MP Jeremy Corbyn called for "appropriate and immediate" sanctions against Israel for "clearly illegal acts".
In a letter to Mr Hague, he spoke of his "shock and outrage" over Israel's actions.
"I visited Gaza earlier this year as part of a pan European Parliamentary delegation and saw for ourselves the continuing destruction from "Operation Cast Lead", the shortages of medicines and vital supplies and the isolation and imprisonment of the people," he said in his letter.
"The continued blockade and under-supplying of Gaza is appalling and also illegal.
"Not surprisingly the people look to other countries to recognise their plight and put appropriate pressure on Israel.
"I would be obliged if you could tell me what actions have been taken by the British Government in respect of the illegal attack and over the safety of British nationals on the vessels."
Fears are growing for two members of the Palestine Solidarity Campaign (PSC), who travelled from Bristol to join the flotilla, the group said.
Sakir Yildirim, from Fishponds and Cliff Hanley, from Southville, had been raising funds for the project and were on the boats.
Nothing has been heard of them since the violence early this morning, spokesman Ed Hill revealed.
The pair flew to Turkey earlier last week and boarded the passenger ship Mavi Marmara.
Both have visited Gaza before. Mr Yildirim, originally from the Blacksea area of Turkey, drove an ambulance to the region in February last year.
Artist Mr Hanley, Secretary of the PSC in Bristol, has visited Gaza once before, in January of this year, as part of the Viva Palestina Convoy.
While the convoy was still anchored at Cyprus on Sunday, Mr Yildirim said: "In the past Israel has been ruthless and unlawful with boats heading for Gaza; they've threatened to fire on them, rammed or boarded them, and imprisoned everyone on board. So obviously everyone is a bit tense right now. But what's different this time is it's a really big project.
"Plus it's backed by the Turkish Government right up the Prime Minister and other Governments around the world. And we have right on our side of course! So I'm sure we'll get there safely.
He added: "I've been lucky enough to have been to Gaza twice before. The injustice is appalling, but their steadfastness is a lesson for us all. The people there are amazing. And the welcome they give visitors is fantastic.
Mr Hanley said: "I'd sooner be over here doing something practical to help Palestine instead of sitting at home and writing futile letters to my MP."
