He said: "There is legislation which concerns causing harassment, alarm or distress.
"But can we police the internet when someone upsets someone else? I don't think we have the resources to do that. We can't have a free-for-all online but we cannot involve the police every time something unpleasant is said."
But Stuart Hyde, chief constable of Cumbria and the Association of Chief Police Officers spokesman on social media, said: 'Social media is increasingly part of police business and the law covers situations where you have comment that goes way beyond legitimate opnion. We don't just deal with people who are famous. People have the right to freedom of speech but it has to be within the law.'
The episode is an embarrassment for Games bosses who dubbed the extravaganza the 'social media Olympics'.
Daley did not make a formal complaint about the series of tweets. Reece Messer was arrested after a complaint from a member of the public.
He was on police bail last night, but he could still face up to six months in prison for offences under the Malicious Communications Act after officers said they were investigating the rest of his Twitter account.
A harassment warning can be issued under the Protection from Harassment Act 1997. It is not a criminal conviction but will appear on an enhanced criminal records check.
Reece's family protested that he is a drop-out who has Attention Deficit Hyperactivity Disorder (ADHD) and 'needs help not punishment'.
His father Norman Messer, 58, apologised to Daley. He said his son has a psychiatric problem and 'badly needs help' but has no incentive to sort out his life because of his lavish benefits.
At his home in Boscombe, near Bournemouth, the carpet cleaner said: 'I'm quite shocked. Reece badly needs help. I'm heartbroken this has happened to him.
"I think the police should be involved, but he doesn't know what he's saying. He just doesn't think about it.
"We've had a long history with Reece. It all started when he was about eight years old, he was quite normal up to that point.
"Then he started going to school, insulting the other children, saying things like 'Your mum's a prostitute' to the other little boys.
"After that there were other problems in school. He's just gone off the rails. He suffers from ADHD. But he won't take his medication.
"I just want to say sorry to Tom Daley and wish him every success in the future."
Mr Messer explained that he and Reece's mother split up when Reece was 12 months, old, and she now lives in Stockport.
The controversy began after Daley and partner Pete Waterfield, 31, came fourth in the synchronised 10metre platform dive.
In a Twitter message, Reece told the young diver whose father died of a brain tumour last year: 'You let your dad down i hope you know that.'
Daley forwarded the abuse from 'Rileyy_69' and commented to his 850,000 followers: 'After giving it my all . . . you get idiots sending me this.'
Thousands of Twitter users rushed to support Daley and identified the abuser.
This provoked a series of messages in which Reece apologised to the sports star but then threatened to 'drown you' and called him a 'cocky t**t'.
One message said: "@TomDaley1994 I'm sorry mate i just wanted you to win cause its the olympics I'm just annoyed we didn't win I'm sorry tom accept my apology."
He added: "please i don't want to be hated I'm just sorry you didn't win i was rooting for you pal to do britain all proud just so upset."
It is understood that the threat of violence led police to arrest Reece at a bedsit in Weymouth.
Daley's close friend and Team GB diving team-mate Tonia Couch, whom Daley watched compete yesterday, suggested the exchange of comments would swiftly be forgotten.
She said: "Tom's a strong boy. He can concentrate on what he needs to do and, at the end of the day, Twitter's Twitter. You don't need to look at it if you don't want to."
Asked what she made of the abuse, she added: "Not much really, neither has Tom. We're just concentrating on the Olympics."
Team GB gymnast Louis Smith said ignoring Twitter is probably the best policy for athletes trying to win an Olympic medal.
He said: "There are just tweets that you do not want to see. Some people are not bothered by negative tweets and they can go about their day, but if you are going to take it personally then do not do it."
- Daily Mail
