It may seem obvious, but Jule Styne, Bob Merrill and Isobel Lennart's 1963 musical Funny Girl needs a very funny leading lady to make it work. And in Sheridan Smith this production - transferring from the Menier Chocolate Factory to the West End - has exactly that and a whole world more.

Smith dazzles as Fanny Brice, the real-life performer, who goes from nobody to somebody with the help of hard work and a prodigious talent for comedy. Fanny is no beauty and she's certainly no leggy chorus girl, but she's got the gift of being absolutely hilarious. It's using her natural abilities to make 'em laugh that she charms city after city and producer after producer until her name is top billing all over the US.

Lennart's book is based loosely on the life of Fanny herself, and it's a fairly simple and slightly flat plot which follows Fanny's rise, paralleled with her rocky marriage to gambling man Nick Arnstein. But it's the lead performer who makes or breaks this show and boy does Smith make it. It's as if she was born for the role. She twinkles, smiles and winks her way into the audience's hearts just like Fanny must have done. Smith's winning connection with the crowd brings the character heartily to life.

Smith is also monumentally funny, and in numbers such as "Cornet Man" - Fanny's big break moment - and "Rat-tat-tat-tat" - where she's wielding a fake gun and dressed as a German general - her comic timing is impeccable. But Smith keeps the gags up whether there's a song involved or not and her double takes, the way she mutters to herself and her physical comedy - brilliantly on show in Lynne Page's neat choreography in "You Are Woman, I Am Man" - make this a performance of a lifetime. She can sing of course, and although a few songs, such as stand out number Rain on My Parade, feel slightly drowned by the orchestra, her voice carries the varied tunes very well.

Michael Mayer's production is whip-crackingly tight and plays out on Michael Pavelka's versatile designs that are framed by a wonky proscenium arch. There's fun work with travelators, too, as the various troupes travel from place to place performing in Ziegfeld's Follies shows across the world. Darius Campbell plays Fanny's no-good husband and he is great. A towering presence over the tiny but mighty Smith, he can't dance, but he delivers his songs beautifully and captures a hard-edged, restless quality to the character that is entirely convincing. He also lets Smith do her thing, giving her the space to shine in their several songs together.

Ultimately, Funny Girl is not about telling the story of Fanny Brice - which doesn't really have enough drama to stand alone. Instead it's about getting Fanny back onstage so she can win the world over once more. And Smith nails that entirely. She will make you laugh, cry and want to see the show again.

Funny Girl runs at the Savoy Theatre until 8 October.