The least amused portrait of Queen Victoria ever created, showing the monarch with brutal realism as an ageing, pouchy cheeked woman with tired eyes, has been saved from export at a cost of more than £1m.

It will go on permanent public display for the first time at the Fitzwilliam Museum in Cambridge. The marble portrait was carved by Sir Alfred Gilbert – best known for the statue of Eros in Piccadilly Circus – between 1887-89.

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The Queen was almost 70, and had finally emerged from a lengthy period of grieving over the loss of her husband, Prince Albert – seen in the locket she wears on her shoulder – when “the Widow of Windsor” had become almost invisible to the public, causing serious concern to the government. Although she would wear black mourning dress for the rest of her long life, she had begun to again attend major public events, including a banquet for 50 kings and princes on 20 June 1887 to mark the Golden Jubilee of her reign.

The portrait, regarded as a virtuoso depiction of ageing skin, soft drapery, crisp lace and jewellery, is the only surviving marble in the UK by Gilbert, who rarely worked in stone. He was commissioned to carve the bust by the Army and Navy club to mark its own golden jubilee, after he made a huge full-length bronze of Victoria for Winchester, which was unveiled in 1887.

The face was based entirely on photographs, but he got his own mother to pose wearing swathes of drapery around her head and neck: “One was Queen of my country – the other Queen of my heart,” he said. Gilbert promised he would complete the sculpture with a marble diadem, but the club never got it.

The bust was sold last year to an undisclosed museum in New York, but the government delayed the granting of an export licence in the hope that a UK institution could match the price. The Fitzwilliam Museum used a recent bequest, and a National Heritage Memorial Fund grant of over £260,000, to raise the £1,077,607 price.

The sculpture will be installed at the Cambridge museum on 20 June – the 181st anniversary of Victoria becoming Queen in 1837.