It is still an enormous muddy hole from which around 50 lorries a day are taking away excavated London clay, but it is a hole the British Museum is quite proud of. In this hole, it believes, is the key to the survival of the collection.

The museum was told on Friday that it could have £10m of lottery cash to help complete ambitious plans for a £135m world conservation and exhibitions centre on the Bloomsbury site's north-west corner.

It was, said the museum's deputy director, Andrew Burnett, "a huge public endorsement of the project" and an important step closer to the finish line.

The cash confirmed by the Heritage Lottery Fund means the museum is still £17m short of the overall cost. The more than £100m it already has includes £22.5m from the last government, £40m from the museum's own resources and £35m from philanthropic fundraisinge.

The 17,000 sq metre extension, designed by Richard Rogers's architectural practice, will have four purposes.

It will provide a dedicated space of more than 1,000 sq metres for the temporary exhibitions the museum is renowned for – past highlights include China's Terracotta Army in 2008 and Moctezuma in 2009 – to replace the converted reading room space that is used at present.

There will also be state-of-the-art science and conservation laboratories to replace the laboratories housed in the basements of 19th-century houses – an arrangement fraught with problems. The lift down to one Egyptology lab, for example, is only big enough for mummified animals and children, not the full-size ones.

Burnett said the building would have a transformative effect on conservation and scientific research. "There should be no limit to the brilliant things that the conservators are able to do," he said.

The building will provide 6,500 sq metres of storage space finally making room, for example, for the museum's unique ethnography collection currently stored off site in Hackney.

One advantage will be logistical. The provision of one of the largest lifts in the UK, into which articulated lorries can drive, should mean museum bosses never again have to watch with their hearts in their mouths as priceless and irreplaceable artefacts are brought in.

"We want to show the collection worldwide and this allows us to do that," said Burnett.

The building site itself does not look very big, as the museum is going so far down, creating three basement levels. "It's dig, dig, dig at the moment," said the museum's project director, Tony Wilson, who added that the mild winter and dry autumn had been a considerable help. "When you're excavating this amount of material, when it's wet it slows the process down enormously."

The work has unearthed nothing more significant than cattle bones and traces of London's defensive ditch dug during the civil war – which is interesting in its own right as it shows just how small London was 350 years ago.

The building will provide better conditions for people such as conservator Kathyrn Oliver, who, in a temporary studio, is putting the final touches to a magnificent statue of Hermes, which came to her in 18 pieces.

In the 1970s, British Museum stonemasons attempted to glue him together. Today's conservators' task is much more scientific and laborious.

After about a thousand hours of work since 2009, Hermes – who belongs to Kew – is still short of a few fingers and toes and, alas for him, his penis, but he looks in remarkably good shape, ready to go on display as part of a planned Olympic trail this summer.

The fundraising for the centre continues. Burnett said he was confident, though not complacent, that the remaining £25m would be raised ready to open the centre – which will amount to about 20% of the museum's footprint – by 2014, with the first major show on Vikings.

"It is the biggest hole in Bloomsbury," he conceded. While the museum is used to big projects – the Great Court reopening in 2000 for example and innumerable other changes, big and small - "this if the first major project for the care of the collection", Burnett said. "It is incredibly important."