Re the Mail article: all that's happened is that the suspect's neighbours decided to talk to the Mail. It's possible the Mail found out where the suspect lived and approached the neighbours, though also quite likely that a neighbour saw the police cars, helicopter etc and tipped off the Mail.
I imagine the police are quite cross given they've told people not to speculate and are keeping the suspect's identity private for the time being.
The Times and Telegraph simply copied the Mail article.
I don't think any of the three newspapers are themselves speculating, but they are publishing information that I imagine the police don't yet want in the public domain.