The work, which will include repairing the 220-year-old roof of the Grade II listed building, will see the museum closed from August 5 until September 12.
This comes after a 2019 structural survey found that the building needed vital work to be carried out to bring it back to 21st-century safety requirements.
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The repairs are being funded by a £1,463,769 grant from the Department for Digital, Culture, Media and Sport through Arts Council England, alongside a £500,000 contribution from Brighton and Hove City Council.
Hedley Swain, CEO of Brighton and Hove Museums, said: “We’re sorry the museum will close during this period as we know visitors will be disappointed.
“The work on the roof is essential to protect visitors and staff, our collections and the building.
“It needs to be carried out at a time when the weather is expected to be dry, to reduce the risk of water damage while the work is being done.
“The summer months are the best time to conduct this work and will mean the closure time will be shorter.
“We hope visitors will understand the situation and take advantage of one of our other venues such as the Royal Pavilion, Hove Museum of Creativity, Preston Manor or the Booth Museum of Natural History.”
In addition to fixing the roof, the overall project – which will not be finished until next summer – will improve the care of the collections housed inside the museum and will boost the visitor experience.
Two Georgian glass lanterns which span the building above the central main gallery will be restored and the original Georgian lighting scheme will be replicated so the whole gallery will be lit by daylight.
The majority of this work will be carried out at various points throughout the year when the majority of the museum will remain open to visitors.
Donna Chisholm, corporate director city services for Brighton and Hove City Council, said: “Repairs to the Brighton Museum and Art Gallery roof are vital for the ongoing maintenance of this historic Grade II listed building.
“The museum is an integral part of our culture and heritage offer in the city, with thousands of school children, residents and visitors enjoying the collections and exhibitions each year.
“The council is pleased to be working in partnership with Brighton and Hove Museums on this project and to provide matched funding for this much-needed work.
“We thank our funding partner Arts Council England for the opportunity to ensure that this building can be used for many more years to come.”
The architects leading the project are Donald Insall Associates.
Olivia Stitson, senior architect at the company, said: “Brighton Museum and Art Gallery is a nationally important building as one of the first purpose-built museums in the country.
“The 1960s roof lantern has reached the end of its service life, and its necessary replacement provides an important opportunity not only to improve safety, maintenance costs and carbon emissions, but make sure we’re passing this much-loved gallery to the next generation.”