My Fair Lady review – patchy West End revival is a star-making moment for leading lady

Watch out classic musical writing teams from the early 20th century: if you've an ampersand to your name, Bartlett Sher is going to try dragging you kicking and screaming into the modern day. Successfully managed with Rodgers and Hammerstein's South Pacific and The King and I, and shortly to take place with a freshly revivified version of Lerner and Loewe's Camelot, It is the second of these duos given a fresh lick of paint in the Lincoln Center Theater revival of My Fair Lady, first seen on Broadway and now sailing into the West End.

Sher's WD40-approach to what is often a rusty and cantankerous musical has gelled well in places. The story, based on George Bernard Shaw's Pygmalion, follows professor of phonetics Henry Higgins who takes working class flower girl Eliza Doolittle under his wing. His objective: to remedy her Cockney accent and regressive ways, which he sees as denigrating and dehumanising.

The contemporary pertinence is hard to avoid – the patronising and privileged trying to educate the working class on how to raise themselves up out of poverty while blithely ignorant to their innate prejudices and assumptions. Two of Higgins' songs, "Why Can't the English" and "A Hymn to Him", betray his almost insufferable ignorance, the kind of morally crusading busybody concocted at the height of the British empire. His nobbishness becomes almost unsalvageable, referring to Eliza as little more than an animal, almost incapable of justifying her own existence thanks to her accent.

Despite being based on Pygmalion, at times it feels more like you're watching some Victorian twist on The Little Mermaid – Eliza, once "bettered" having been robbed of her voice, her very personality, thanks to some unjust bargain made by those with ulterior motives. Those expecting a beloved tribute to Hepburn and Harrison's movie may be surprised.

As isn't all that shocking, Sher brings out cracking performances from his cast: Harry Hadden-Paton, back on home soil after playing Higgins on Broadway, is aloof, flappable and flawed – like a linguistic Phileas Fogg about to embark on a lexiconic thrill ride. Vanessa Redgrave brings an ageless charisma to her scenes – pulling off a similarly irresistible charisma to Maggie Smith's dowager countess in Downton.

The break-out star, as well she should be, is Amara Okereke's Eliza. Okereke's amassing a roster of cracking credits – Wendla in Spring Awakening, Cosette in Les Misérables, Laurey in Oklahoma! or Polly Brown in The Boy Friend, but this is her largest and certainly most accomplished turn. She shimmers like sunshine as she sings to the dawn in "I Could Have Danced All Night", and grounds the whole three-hour show with a faultless depiction of someone simply wanting to get ahead in the world.

But it doesn't all click: despite what should be a majestic, rousing atmosphere conjured by a mammoth 40-piece orchestra, the show never really rises to match the grandeur of the Coliseum stage – the largest in the West End. A few numbers manage to land – Christopher Gattelli's bawdy choreography during "Get Me To the Church On Time" being a particular highlight. But the auditorium has an annoying tendency to swallow up what is, for large passages, essentially an intimate comedy musical between a small coterie of characters – Higgins, Eliza, wizened and amiable Colonel Pickering (an exquisite Malcolm Sinclair) and the unflappable housekeeper Mrs Pearce (Maureen Beattie – the dictionary definition of comedy foil in almost every scene).