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These pictures show the latest plans for the new Museum of London on the site of a former market in West Smithfield.

The plans, which are going on show at the Farringdon site and at the current museum at London Wall on Friday, include ideas for making the building a 24-hour destination to mirror near-neighbours like the meat market and Fabric nightclub.

Museum director Sharon Ament said: “We will be inhabiting what I believe is one of the most 24-hour parts of London.

“Do I really think we’ll be opening at 3am? Maybe sometimes. Who knows, maybe we’ll have an all-night festival a couple of times a year?”

She said one of the potential late-night venues is a cafe and bar on the site of a 19th-century coffee house.

“We have uncovered the remains of a Victorian cafe called the Temperance Cocoa Room. We might take away the word temperance for obvious reasons but we’ve gone into that part of the building and the original Victorian tiles are still there. It is amazing, and so obviously we want to make this the Cocoa Rooms again, and that could be a place that goes through the night.”

As the plans go on show, it has been revealed that the cost of the ambitious scheme has shot up by more than £80 million.

The transformation was originally expected to cost £250 million but recent studies have found that more work is needed to bring the 19th-century buildings up to date.

Ms Ament said she was “very confident” the final £44 million would be found to meet the £332 million budget and the new building would open as planned in 2024.

She said the “complexity of the building” had caused the budget to rise. “It is to do with things like waterproofing a building that hasn’t needed to be water-proofed, it is to do with engineering.”

A planning application should be submitted later this year.

Expected features are likely to include a dome on top of the general market being lifted to provide a landmark directly above a set of spiral escalators that will twist underground, carrying visitors into the rooms that used to store produce when it was a working market.

It may also include proposals to link the spaces below ground with a tunnel under the Thameslink tracks that run below the site, a sunken garden and a well reaching down to the waters of the River Fleet, which flows beneath the streets of Farringdon.