Barry Sweeney, whose son Liam was among the 298 people killed, spoke of his anger and frustration at not knowing what had happened to the 28-year-old's body.
He and his wife Angela were among seven of the 10 families of British victims of the crash to attend an hour-long meeting with Cameron at his Downing Street office on Tuesday.
"I feel very angry and frustrated. It would be nice if they could just stop fighting for a little bit so that we could get all our boys and girls home," Sweeney said.
Western governments say the evidence points to the plane having been shot down by pro-Russian separatists.
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"Mr Cameron was very humble. He answered every question that was asked of him. He brought a few experts in to talk about crash sites and how the airplane might have come down," Sweeney said.
"We basically asked Mr Cameron just to help. The talking, I suppose, has got to stop and the doing has got to be done."
"It's very difficult but unfortunately we are going to have to wait to find out," he added.
Liam Sweeney was travelling with fellow Newcastle United fan John Alder to see the English Premier League football club's pre-season tour in New Zealand when the plane came down.
A Downing Street spokeswoman said Cameron has expressed his condolences to the victims' families.
"He made clear that the government was determined to do all it can to support them over the coming difficult months, from ensuring that their loved ones are brought home as soon as possible to bringing justice to those responsible for shooting down the passenger jet," she said.