The group, Muslims against Crusades, was behind a poppy-burning protest on Armistice Day.
Officers said talks were continuing on whether protests at other nearby locations would also be blocked.
The English Defence League had said it would hold a counter- demonstration if permission were granted.
Five thousand police officers will be on duty on the day.
Assistant Commissioner Lynne Owens said that negotiations with the groups were "on-going", but pledged that the wedding would not be disrupted.
She said there would be 70-80 close protection teams for VIPs on the day, 29 April.
Police have already begun searching central London for explosives.
Scouring route
Officers are scouring every inch of the route to Westminster Abbey, while dogs have also been checking bins and lamp-posts for bombs.
At a briefing on security arrangements, Ms Owens said 60 people currently on bail from prison would be banned from Westminster on the day of the wedding.
Criminal activity would be dealt with "quickly, robustly and decisively so that it's a happy event for everybody else who intends to be there", she added.
As well as the Royal Family, 50 heads of state are attending the ceremony, which it is anticipated will be watched by up to two billion people on television.
Scotland Yard said it had no intelligence of a specific terrorist threat to the wedding so was not currently in a position to impose anti-terrorism stop-and-search powers, said the BBC's Danny Shaw.
Police have powers to ban any major protests along the main route that Prince William and his bride-to-be, Kate Middleton, will take.
But they are unable to rule out "static" protests taking place at other nearby locations in central London.
Officers at Scotland Yard were contacted by the ultra-nationalist English Defence League, which said it wanted to protest if the Muslims Against Crusades' proposed action went ahead.
Poppy-burning
In March this year a member of Muslims Against Crusades was fined £50 for burning poppies at an Armistice Day ceremony.
Emdadur Choudary, 26, burned two large plastic poppies during a two-minute silence in west London on 11 November.
The group's website calls on Muslims to disrupt the wedding, describing senior members of the Royal Family as "enemies to Allah and his messenger".
Sgt Richard Brandon explains how a police helicopter will provide security and surveillance
Ms Owens told the BBC police saw the wedding as a "day of celebration".
"What we will be doing is making sure that no protest disrupts that celebration for the Royal Family.
"What we have to do whenever we're deciding about whether there can be a protest, if they're asking to protest in the area around Parliament, it is defined by a very set definition of law - we have to authorise a demonstration but we can put conditions on that demonstration.
Helicopter cameras
"It's that negotiation process that we're engaged in at the moment. But [people] should be absolutely reassured that it won't disrupt the day and we'll have a very safe and happy celebratory event."
The London Metropolitan Police Air Support Unit has said it will deploy a helicopter fitted with high definition video cameras to provide support to police on the ground.
Quilliam, a counter-extremism campaign group, dismissed both Muslims against Crusades and the English Defence League as "publicity-hungry fanatics" with few followers.
Ghaffar Hussain, Quilliam's head of training and outreach, said they were "extremist" groups, "whose only aim is to divide our society and to sow suspicions and hatred between Britain's different peoples".
Last week, more details of the royal wedding were released by Clarence House, including the exact timings of the event and the route of the carriage procession.
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