Republic CEO Graham Smith said those who voted to sever ties with the trading bloc would be left “feeling short changed” by “how little control” they take back.
He said royal prerogative powers would see more power given to the Prime Minister than ever before.
Mr Smith told Express.co.uk: “I think that the sentiment behind Brexit for a lot of people is to do with democracy and the phrase was ‘taking back control’.
“A lot of people will probably be disappointed by how little control they will take back, where control is shifting is from perhaps, in certain circumstances, from Brussels to Westminster.
Graham Smith said Brexit meant handing EU powers to the Prime Minister
A lot of people will probably be disappointed by how little control they will take back
“When I say Westminster, I mean Downing Street.”
He said a yearning for more democratic power could lead to growing support for his campaign group’s mission to oust the monarchy.
He said: “I think that the sentiment will not go away and I think people will still want to – [now that] they [have] got an appetite now for a more democratic power, I think that’s not going to go away.
“And I think they’ll be feeling shortchanged in a few years time and so there’s going to be an opportunity for us.”
Monumental moments of Queen Elizabeth's reign Wed, February 8, 2017
Britain's longest-reigning monarch is celebrating her Sapphire Jubilee after taking the throne 65 years ago. Here is a look back at the monumental moments that defined her reign
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Monumental moments of Queen Elizabeth's reign
Nigel Farage was one of the more prominent Brexiteers during the referendum campaign
Mr Smith called for the UK to have an elected head of state independent from the Government, which he said would scrutinise it more effectively.
He then rebuked the Royal family, claiming he could not think of a “single reason” for keeping the monarchy going.
Mr Graham said: “I’ve never heard a good reason for keeping the monarchy, I can’t think of a single one.
“There’s plenty of myth around it, people say that everyone likes it and that’s not true – most people don’t care. People say it’s good for the economy, which also isn’t true, there’s no evidence.
“People say that the Queen keeps power away from politicians and the opposite is true, there’s a lot of power in the hands of the Prime Minister.
“People might enjoy it on the day of a wedding or a jubilee but I think that’s a pretty flimsy argument for what is our head of state.”
The comments come despite a recent YouGov poll revealed 68 per cent of participants believed the monarchy was good for the country.
Queen Elizabeth II became the UK’s longest-reigning monarch in 2015 and has now been head of state for 65 years.