Nor did they check publicly available records of Eric Bellquist's running routes on a website which do not show any runs in which he has crossed Putney Bridge.
Bellquist, 41, was dramatically hauled away in handcuffs from his home in Chelsea, West London, last week after police released CCTV footage of the incident and appealed for members of the public to identify the jogger.
Bellquist protested his innocence, insisting he was in the US at the time.
Asked whether the force would be issuing an apology to Bellquist, a spokesman said last night: "There were reasonable grounds to arrest the man in connection with this offence.
"He was subsequently released with no further action to be taken."
But when asked whether they had any more evidence other than a tip-off prior to the arrest, a spokesman said they had a "good response to the appeal".
Last night, Bellquist's friends insisted the police should apologise. One told The Mail on Sunday: "Eric was as horrified as everybody else about this attack and had absolutely nothing to do with it. He has been through hell. He was woken up by the police, dragged out of his house and thrown into a cell for hours. He is very worried about his reputation and deserves an immediate apology."
Police have renewed their appeals for people who might recognise the attacker from CCTV footage to come forward.
The video clip has provoked widespread outrage and shows the woman walking across the bridge to work when she is pushed into the road by a male jogger wearing a grey T-shirt and dark shorts. She narrowly avoided serious injury after an approaching double-decker bus swerved to avoid her head as she lay inches from its wheels.