Broadway star Audra McDonald returned to London tonight for her first solo show in some 15 years. The six-time Tony Award winner, famed for her Broadway roles in shows as diverse as Ragtime, Porgy and Bess and her most recent Billie Holiday vehicle Lady Day (reviewed here) played a one-off date in the intimate Leicester Square Theatre, which sold so quickly that an additional matinee was swiftly added. Yet her name remains unknown to the majority of the population – tonight's audience was a mixture of musical theatre fans and performers (Elaine Paige and original Billy Elliot star Haydn Gwynne in their midst). But for those of us already initiated in McDonald's talent, it was a rare opportunity to see the Broadway star up-close and personal, singing a typically versatile range of songs and styles in her stunning soprano voice, and to have a small insight into her home life and hopes for the world.

Entering without fuss to a rock-star reception from an audience obviously familiar with her work, McDonald is unfazed by the vocal adoration, and has a natural connection to the audience, chatting as if we were old friends. Her ninety-minute set includes a diverse selection of musical theatre numbers, some well-known favourites and other lesser-known songs from the 'new' generation of Broadway composers. The programme varies from Rodgers & Hammerstein's The Sound of Music to Adam Gwon's Ordinary Days and from Lerner and Loewe's My Fair Lady to Jason Robert Brown's Songs for a New World, to name but a few. McDonald gives the traditional musical theatre biggies the emotional and stylistic gravitas they deserve – 'Maybe This Time' is full of determination, while 'Climb Every Mountain' has layer on layer of truth. But she tempers the mood of the concert with humorous and informative anecdotes in between numbers. McDonald starred as the Mother Abbess in an American TV version of The Sound of Music – 'I like to think she was from the sunnier side of the Alps!' she jokes, while telling the audience that her daughter texted her ‘review’ of her big number which was to ask where to find clean sheets at home. No wonder McDonald remains refreshingly grounded for such an acclaimed talent.

McDonald is always totally in the moment – either as a character or in an emotion – and is a great storyteller, getting to the truth of every lyric. McDonald talks movingly about deep issues – including one of her own country's 'dark moments', when a group of black youths were falsely accused of raping two white girls, as explored in Kander & Ebb's final musical The Scottsboro Boys, from which she sings the simple yet moving 'Go Back Home'. The breathtaking 'I'll Be Here' from Ordinary Days – a personal tale of the cost of 9/11 – is also thrillingly rendered. The Jule Styne and Comden & Green number 'Make Someone Happy' from the 1960 musical Do Re Mi provides McDonald's mantra for life. Its lyrics also suggest that there's more to a performer's life than being on stage: although 'the sound of applause is delicious,' at the end of the day 'someone to love is the answer' for true fulfilment. McDonald chats openly about her personal life and relationships, especially with her daughter – her Sondheim choice was A Little Night Music's 'The Glamorous Life' which talks about a daughter separated for long periods from her actress mother.

There’s a simplicity yet sincerity about McDonald throughout the evening. Porgy and Bess’ 'Summertime' was sung without microphone, displaying the clarity and beauty of McDonald’s natural vocal tone. And although the evening features just McDonald and her musical director Andy Einhorn on piano, both the vocals and the piano fill the intimate space with great richness. McDonald – ever the ambassador for humanity and equality – leaves us with 'Over the Rainbow', which this Judy fan sings 'for hope everywhere'. McDonald leaves London for a 5.45am flight to NYC tomorrow morning to go straight into rehearsals for her latest Broadway musical Shuffle Along, but she returns in June to make her West End debut in a 10 week transfer of her Broadway hit Lady Day. It looks like she’s finally about to get the UK acclaim she so richly deserves.