Those who gathered to express sympathy said the 46-year-old band member, who was from Friarstown, Kilmallock in Limerick, was a attractive person and they were shocked and saddened at her sudden death.
Police also confirmed to the media that a report was being compiled for the coroner's office to investigate the cause of O'Riordan's death.
O'Riordan auditioned to become singer of the Smiths-inspired band The Cranberry Saw Us, formed by brothers Noel and Mike Hogan, in 1990.
"To all those who follow and support Irish music, Irish musicians and the performing arts her death will be a big loss", Irish President Michael Higgins said, according to The Irish Times. Taoiseach (Irish Prime Minister) Leo Varadkar called her "Limerick's greatest ever rock star", and that her band "captured all of the angst that came with your teenage years".
The Cranberries formed at the end of the 1980s and had global hits in the 90s with songs including Linger, Zombie and Dream.
O'Riordan was born on September 6, 1971 in Ballybricken, southwest Ireland.
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"I had anorexia, then depression, a breakdown", she admitted in a 2013 interview.
The Cranberries broke up in 2002, when O'Riordan left the band - but not before they had sold some 35 million albums worldwide. More than a year after it was first released the band's album topped the charts. The Cranberries and O'Riordan are also dominating Amazon's ranking of physical CD and vinyl sales, claiming all of the top ten slots, with O'Riordan's 2009 solo album, No Baggage, ranking fourth with sales up more than 200,000% in the past 24 hours.
The Cranberries released the acoustic album "Something Else" in 2017 and had been due to tour Europe and North America.
In India, the singer enjoyed a great fan following. It threw into question what a voice could sound like in that context of Rock. Last year Chester Bennington, and early this new Year Dolores O'Riordan. "Linger" was probably the Cranberries song I sang along to the most when I was in high school, whenever I was pining over my latest crush. "On tour it's, like: "'room-service", she said of the comeback. She spoke publicly about contemplating suicide and her bipolar disorder, which she struggled with for years before being diagnosed in 2015.
Publicist Lindsey Holmes said O'Riordan died suddenly while in the United Kingdom capital where she was recording.