A British family of 12, including a baby and two grandparents one aged 75, are believed to have gone to Syria after the family reported them missing, police said on Wednesday.

The family, from Luton in Bedfordshire, central England, have not been seen since mid-May when they failed to return home after a holiday in Bangladesh.

Police said they had flown to Turkey and were then due to travel on to Britain, but were instead reported missing by a relative.

"There is a suggestion that the family may have gone to Syria, however police have so far been unable to corroborate that information," Bedfordshire Police said in a statement.

Some 700 Britons are thought to have gone to Syria, many to join the self-proclaimed Islamic State of Iraq and al-Sham (ISIS) militants who have taken control of large areas of the country and neighboring Iraq.

Last month, 12 members of another family, three sisters and their nine children from northern England, were suspected of travelling to Syria to join the militant group.

Prime Minister David Cameron has said Britain needed to confront the ideology that was luring Britons to Syria and has said his government would step up measures to confront those who espouse extremism at home.

"We are devastated by the disappearance of these 12 and are very concerned for their safety," the family of the missing Luton family said in a statement.

"This is completely out of character and we are very worried of the danger they may now be in. This just does not make any sense. We can only think they have been tricked into going there, it is no place for elderly or young people."

The grandparents, Muhammed Abdul Mannan, 75, and his wife Minera Khatun, 53, both had health issues, police said. The BBC said it understood Mannan had diabetes and his wife had cancer.

The group included the couple's daughter and sons, and three children aged between one and 11.