A street party for republicans wishing not to celebrate the royal wedding has been banned by a north London council.

The anti-monarchy pressure group Republic has complained that its application to close a street in Covent Garden for its party has been turned down by Camden council. The council claims that it told the group to provide a management plan and consult local residents and it failed to do so.

The decision left Republic vowing to take court action. Its executive officer Graham Smith complained: "This is a disgraceful attack on the rights of republicans to make their voice heard and to hold a fun and peaceful event. Camden council is allowing a few vocal residents and businesses to veto any event they do not support ... (It) is seeking to silence and marginalise us without any legitimate reason.

"We can only assume this is a politically motivated ban and we will challenge it all the way."

The organisation may be able to claim the support of two unlikely recruits. David Cameron told readers of the Sun that the wedding on 29 April would be a chance for everyone to come together and celebrate the great things about the country: "People who want to come together to celebrate with their neighbours should go ahead. We've done our bit by ripping up red tape."

Joining in, the Health and Safety Executive (HSE) insisted that royal wedding party organisers should not be fobbed off by "jobsworths" trying to prevent them. The organisation said it was concerned that health and safety would be used as an unfounded excuse to stop celebrations.

Judith Hackitt, the chair of the HSE, said: "Volunteers should feel confident to organise celebrations, taking simple measures based on common sense without having to worry about obligations under health and safety law at all. I want to encourage people to challenge those who tell you something can't be done for health and safety reasons – it's too easy an excuse to trot out.

"There's nothing in health and safety law to prevent anyone from celebrating the royal wedding – in fact, HSE encourages everyone who wants to throw a party to go right ahead. If someone tells you that you can't have a get-together to mark the nuptials of Prince William and Kate, then challenge them. Health and safety is about looking out for any legitimate things that might spoil people's fun on the day, not to stop people doing anything at all."

The organisation's website says that while organisers should consult councils to secure road closures and permission to sell alcohol, those organised on a non-commercial basis would not fall foul of restrictive rules and regulations preventing them from going ahead. The prime minister claimed on Monday that about 4,000 street parties were known to be going ahead – though that is many fewer than at the time of the wedding of Prince Charles and Princess Diana in the summer of 1981.

A spokeswoman for Camden council said that permission for Republic's celebration in Earlham Street, just off Shaftesbury Avenue, had been refused: "We asked them to come to us with a management plan and after consulting local residents and they did not do so. There were objections from local residents and businesses and significant concerns from the police about the potential for disorder. We have allowed other street parties."