A family of 12 including two grandparents with health problems and a baby are feared to have travelled to Syria.
The group from Luton were reported missing when they failed to return home from a holiday in Bangladesh.
Relatives said the disappearance does not make any sense, adding that they "can only think they have been tricked".
Bedfordshire Police named those who are missing as: Muhammed Abdul Mannan, 75, his wife Minera Khatun, 53, their daughter Rajia Khanom, 21, sons Mohammed Zayd Hussain, 25, Mohammed Toufique Hussain, 19, Mohammed Abil Kashem Saker, 31, his wife Sheida Khanam, 27, Mohammed Saleh Hussain, 26, and his wife Roshanara Begum, 24, along with three children, aged between one and 11.
The three children have not been named.
Mr Mannan was described as "frail" and reportedly suffers from diabetes, while his wife is understood to have cancer.
In a statement relatives of the group said they "can only think they have been tricked".
They said: "We are devastated by the disappearance of these 12 and are very concerned for their safety. "This is completely out of character and we are very worried of the danger they may now be in.
"Muhammed Abdul Mannan is elderly and both he and Minera Khatun have health issues.
"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.
"We would urge any of them to please make contact with us or the police to let us know they are okay."
The party initially travelled to Bangladesh from Heathrow via Istanbul on April 10, before flying back to the Turkish city on May 11.
They were due to come back to London three days later but failed to return and were reported missing by a relative on May 17.
A police spokeswoman said: "There is a suggestion that the family may have gone to Syria, however police have so far been unable to corroborate that information.
"Police are continuing with their inquiries and are working with relatives who are still in the UK."
Community leader Ashuk Ahmed said he had known the family for around 30 years.
He said there were suggestions within the community that a woman in the group might have been "radicalised".
Mr Ahmed told the Press Association: "The family was under the impression they were travelling to Bangladesh. It was planned as a genuine family visit.
"The old man is frail and the wife is suffering from cancer. They were told they were going to Bangladesh on a family visit. I believe they stopped in Turkey on the way back.
"When they didn't turn up in the UK (other) family members raised the alarm. They were told they may have crossed into Syria.
"The community is in shock. The boys were all running successful businesses."
He added that he had heard that a member of the group had contacted relatives two weeks ago.
"I was told by people in the community that they made a phone call to family members and told them not to worry and that they were all safe."
Last month fears emerged that three British sisters had travelled to Syria with their nine children aged between three and 15.