Detectives believe she may have been kidnapped as she walked home from a nearby tram stop after spending the day in the city.
Police were last night interviewing a man in connection with the murder but he has not been arrested.
Lauren, who was a pupil at Abraham Moss High School, was reported missing in the early hours of yesterday when she failed to return from central Manchester.
Four hours earlier, at 9pm, the fire brigade was called to a blaze on Moss Bank, Crumpsall, which they thought was burning rubbish. As the flames died down they found the body.
It is understood police discovered clothing and jewellery belonging to Lauren at the scene.
A post-mortem examination was held yesterday but the results were not released. It is understood the body was so badly burnt that formal identification would only be possible through dental records.
However, residents in the street where Lauren lived named her as the young victim.
One neighbour, Carol Power, said: "She was such a lovely little girl and very, very pleasant to have around.
"My grandson was often out playing with her and I know she was as good as gold. The family are absolutely devastated."
Another neighbour said of Lauren: "You used to see her around quite a lot and she had a 16-year-old boyfriend, but I think they may have split up quite recently.
"I've got kids myself and when I heard how it might have happened, on the way back from the tram, I thought there but for the grace of God. I'm sure her mum Jill will be in pieces."
Another local resident, who came to lay flowers said: "We have got five daughters and it really scares me to think something like this could happen.
"Only last week a man tried to coax my nine-year-old away from her playmates just up the road. And it makes me shiver to think it could have been her they found this morning."
Garage owner Kenneth Williams, 62, said: "I got a telephone call from the police last night saying that a body had been found and would I open the garage so they could get access to the back."
Yesterday, flowers were laid outside the garage, MBM Motors, and it was sealed off as police forensic teams examined the wasteland behind.
A small piece of parkland next door and an embankment on the tram line which runs alongside were also painstakingly searched by officers.