I'm pretty sure that there has been an extensive thread on the East Dulwich Forum about the woman-and-imaginary-baby scammer that Marthasmum describes. From memory ,a lot of the features match: plausibly 'respectable' in demeanour, claims to live in the same street, needs money for utility (gas, electricity), baby referred to but not with her.

I couldn't find the thread but, if anyone's better at searching than me, they're welcome to have a go.