Carl Worrall, 49, of Pyle Street, Newport, Isle of Wight is accused of a public order offence.
Jack Stevens, 26, of Oxford Street, Long Eaton, was charged with criminal damage in connection with the throwing of a flare.
Nottinghamshire police commissioner Paddy Tipping said the cost of policing the march will probably reach Â£200,000.
About 100 EDL supporters attended, with several hundred people gathering to oppose the protest.
Mr Tipping said he will be asking the Home Office to introduce tougher laws to stop disruptive protests.
"We have to be clear that demonstrations like this are disruptive and they do cause concern in the wider community," he said.
"I am not sure we have got the balance right. People have a right to demonstrate but normal citizens have a right not to have their lives disrupted."
Police said of four other people arrested in connection with the demonstration, one was bailed and the other three released without charge.
They said they had received no reports of injury or assault during the march.
The force was supported by 21 other police forces - including specialist officers, police dogs and mounted officers.
Two men arrested after a march organised by the English Defence league (EDL) in Nottingham, have been charged.