Akeel Nanabawa, his wife Hannaa Vorajee and their four-year-old daughter Sara Nanabawa were returning home to the UK when they died.
The Boeing 787 Dreamliner crashed shortly after take-off on Thursday in what is one of the deadliest plane accidents in terms of the number of British nationals killed.
The aircraft struck a medical college hostel in a residential part of Ahmedabad, killing 241 of the 242 people on board.
The sole surviving passenger was Briton Vishwash Kumar Ramesh.
Air India said the plane was carrying 169 Indian nationals, 53 Britons, seven Portuguese nationals and one Canadian.
Mr Nanabawa ran a recruitment firm, while his wife volunteered at a local Islamic school in Gloucester – where they lived.
Members of their family have flown from the UK to Ahmedabad following last week’s tragedy.
“There is no UK leadership here, no medical team, no crisis professionals stationed at the hospital,” said a family spokesman.
“We are forced to make appointments to see consular staff based 20 minutes away in a hotel, while our loved ones lie unidentified in an overstretched and under-resourced hospital.”
Another family member said: “We’re not asking for miracles – we’re asking for presence, for compassion, for action.
“Right now, we feel utterly abandoned.”
The family also have several of what they described as “key concerns”, including a “lack of transparency and oversight in the identification and handling of remains”.
They called for a “full crisis team” at the hospital within 24 hours, a British-run identification unit, and financial support for relatives of the victims.
A local doctor had “confirmed” the delays in releasing the bodies were “linked to severe under-staffing”, according to the families, who also called for an independent inquiry into the UK Government’s response.
“Our loved ones were British citizens. They deserved better in life. They certainly deserve better in death,” the statement added.
Among the Britons believed to have been on the Gatwick-bound flight was Arjun Patoliya, who had flown to Gujarat from London to scatter the ashes of his wife, Bharti.
Others included radiologist Dr Prateek Joshi, from Derby, and sisters Dhir and Heer Baxi, couple Fiongal and Jamie Greenlaw-Meek, and Raxa Modha, Rudra Modha and K Mistri, from Wellingborough.
UK air accident investigators are already in India and are assisting the Indian authorities.
