Before the summit, Sir John, president of ACPO, told BBC Radio 4's Today programme there were "many legal and practical difficulties" with the plan.
The prime minister suggested in a speech last week that police officers could march offenders to a cashpoint to make them pay a fine - but now the Home Office is looking at ways to make drunks pay up at a later date.
"The collection of cash is not a practical idea and we don't have that provision in the British police force," he said.
Home Office Minister Charles Clarke acknowledged that the idea of trying to extract the cash on the spot "was not seen by officers as the best way of proceeding".
The U-turn prompted derision from shadow home secretary Ann Widdecombe, who said Mr Blair had "made a complete fool of himself" by announcing plans before consulting police chiefs and experts.
" Did it really need five chief constables trooping into Downing Street to tell the prime minister that his plans were flawed?" she asked.
"Anyone with an ounce of common sense could have figured out that this scheme is unworkable."
Fixed penalties
But Mr Blair's spokesman insisted "the broad reaction from the police at the meeting was positive to the idea of fixed penalties", whereby offenders would be issued with notices to pay at a later date, like speeding tickets.
He said Mr Blair was keen to pursue the idea, and look at "hard-edged, practical ways" of sending a tough signal to louts.
Minister Charles Clarke would be talking to police organisations find a "simple, fast and hard" way of tacking the problem, and if necessary the government would bring in new legislation.
Before the summit, Sir John, president of ACPO, told BBC Radio 4's Today programme there were "many legal and practical difficulties" with the plan.
"I think that the whole process of thinking that people who are raging drunk, or indeed those who are being disorderly or even violent, can be made quiescent to go to a cashpoint, will cause us some difficulties," he said.
The plan would increase the potential for false allegations to be made against police officers and, worse, that criminals might impersonate officers, he added.
The police officers made it clear at the summit that a tougher approach to street violence would require extra funding and extra officers.
"We are obviously hopeful some allocation will be made available to us," Sir John said.
Higher police presence
The summit also discussed the way that crime statistics are collected, and looked at a series of other measures to stop town and cities being plagued by drunken hooligans.
They agreed to look at increasing police presence in high crime and disorder areas, and use intelligence more effectively to identify perpetrators.
New by-laws to focus on alcohol abuse in public areas were also mooted.
Mr Clarke said: "I think the central message that I would want to send out of this seminar was the determination of all concerned - the politicians, the police, the others involved - to work together to create a climate in our communities where violent crime and disorder are not tolerated."