The project’s budget has increased £72m from the original £250m price tag.
The museum said this followed “detailed studies on the historic buildings, which date back to the 19th Century, and the increased investment needed to bring them back into use, as well as the design solutions required to adapt them into a world-class museum.”
The City of London Corporation has agreed £192min funding alongside £70m from the Mayor of London.
The museum has already raised £26.5m of the remaining £70m and is aiming to submit a planning application by the end of this year ahead of a 2024 opening date.
Latest designs go on display within the currently derelict West Smithfield site this week.
They form one of the biggest cultural projects underway in Europe from a design team led by Stanton Williams and Asif Khan with Julian Harrap Architects.
Sharon Ament, Director of the Museum of London, said: “The new Museum of London will transform what a museum should be as we will become a shared space in the middle of it all, in the middle of London and in the middle of ideas and our shared history.
“As people will see from our latest design concepts, it will be a totally porous space available night and day to welcome all of London’s visitors.
“It’s been remarkable working with such a creative group of architects and designers who have delved deeply into an equally remarkable set of buildings.
“We’re looking forward to sharing the plans and hearing people’s feedback which we’ll reflect on as we progress into creating more detailed designs in the coming months.”