The Andrew Lloyd Webber musical originally opened in London in 1993, with Glenn taking on the central role of Norma Desmond, a fading film star who ensnares a down-on-his-luck screenwriter, when it transferred to New York the following year (94).
On Monday (04Apr16) Glenn returned to the role which won her a Tony Award in 1995, this time at the British capital's London Coliseum Theatre.
British critics gave the veteran Hollywood superstar impressive notices for her part in the show, which is based on the 1950s film noir of the same name.
"It might be 20 years since she bagged a Tony in this part, but I wouldn't bet against her scooping a few shiny new gongs this time round," Holly Williams from British theatre website WhatsOnStage wrote.
Michael Billington of Britain's The Guardian newspaper also praised the star, writing, "Close also delivers the big lines not with a camp flourish but as if they were sincerely felt."
Rod MCPhee of the Daily Mirror added his own rapturous review, as he wrote Glenn,"Masterfully belts out the show's biggest numbers, and earned rapturous applause as a result. Her first musical in London's West End proves that she's far from a fading star."
What criticism there was of the show's opening night mainly centred on the production of the show, rather than its leading lady who attracted almost universal praise.
Speaking to the BBC after her performance Glenn said, "Norma Desmond is one of the best parts ever written for a woman. It's a phenomenal show, it's such an exciting journey and it has been the best adventure. I feel so lucky. I am on such an emotional high, I've never had this kind of response."
Also starring Michael Xavier as Joe Gillis, the film scribe who becomes entangled with Desmond, the production runs at the London Coliseum until 7 May (16).