Precious, possibly abandoned cat?

We'd been hearing a cat miaowing for a few days, and it seemed distressed, but whenever I tried to look I could never figure out where it was. On this day I was in front of the house with my granddaughter when we heard it again. We went looking and started calling. Lo and behold, this cat came running to us, jumping from one of the flats in the block nearby and miaowing like mad! It couldn't jump the fence so I had to lift my granddaughter up for her to get the cat, she let herself be picked up without protest, and Lu named her Precious.
We think she's a girl. She's in very good condition so hopefully owners are just on holiday? We have fed her and she follows us but dare not go inside the house, as our cat lives there.
Can't tell if she's a moggy or a breed cat. She's very vocal, super friendly, the fur is silky and incredibly soft!!! If anyone knows, let me know. A friend suggested she might be a Maine Coon...
If she's still homeless when it gets colder I might think of letting her in the house, provided her cat and my cat are on friendly terms (I'm slowly introducing them to each other but Precious hisses like mad at my elderly cat, who in turn seems very relaxed about the whole thing)
Update! He's a boy! Full story & new name here: wp.me/peZxVi-2Ms