Alex Deane and other trustees are currently trying to secure £1 million to fund the project which would tell the story of “one of the most significant events in our lifetimes”. Mr Deane, a prominent Leave campaigner, has insisted the museum will be strictly apolitical and tell the story of the campaign and historic vote without bias.
Despite this it has received “hostile responses from continuity Remainers”, he said.
But Mr Dean, the executive director of the Grassroots Out campaign in 2016, insisted they are still “definitely reaching out to Remainers”.
Speaking to Express.co.uk, he said: “All will be welcome when it opens.
“It’s going to be a ranging, engaging, informative experience for everyone who comes.
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News of the project emerged last week after it was granted charitable status.
The trustees are seeking to generate £400,000 to buy a home for the museum.
They want another £250,000 to set it up and a further £350,000 as a strategic financial reserve.
It is being championed by prominent Leave campaigners who want to tell the story of Brexit “before items and stories get lost”.
It has yet to have public endorsements from pro-Europeans, but the trustees say they are keen to work with anyone.
But, the plans have been attacked on social media.
One wrote: “A lot of money when the whole UK could be a museum of Brexit in a couple of years.”
Another raged: “I liked how it offers ‘EDUCATIONAL RESOURCES’.
“If they’d availed themselves of some of them before then there wouldn’t be any f**king need for a bloody Museum of Brexit.”
A Q&A on its website says both sides of the Brexit debate need to be presented “fairly and in a balanced way”.
Speaking last week, Mr Deane said: “There is a tremendous story behind this that deserves to be preserved.
“Unless we act fast, much of the material from the referendum will be lost. Our objective is to plug that gap at the time when it is easiest – right now, while memories are fresh.”
Other trustees include Lee Rotherham, a former director of special projects at Vote Leave, Thomas Borwick, Vote Leave’s former chief technology officer, Jim Reynolds, the honorary secretary of the Campaign for an Independent Britain, and Gawain Towler, a former director of communications for Ukip.
The museum is intended to include a library and an archive, while its website sets out how people can contribute items, such as correspondence, diaries and campaign material.