Dublin-born Sir Michael, who worked in TV, film, theatre and radio in his six-decade career, died peacefully in hospital late on Wednesday after a bout of pneumonia.
Hannah Essex of the Society of London Theatre said the theatre world has “lost an incredible talent” and described his impact on the arts as “immeasurable”.
Sir Michael starred in six of the eight Harry Potter films as headmaster Albus Dumbledore. Daniel Radcliffe, who played the boy wizard, praised Sir Michael as “one of the most brilliant, effortless actors” he had ever worked with.
He added: “Despite his immense talent, the thing I will remember most about him is how much fun he had doing his job. He was silly, irreverent and hilarious. He loved his job, but never seemed defined by it.
“With his loss the world just became considerably less fun.” Sir Michael was awarded four TV Baftas during his career for his roles in BBC family drama Perfect Strangers in 2002, in Channel 4’s Longitude in 2001, the BBC’s Elizabeth Gaskell adaptation Wives And Daughters in 2000 and The Singing Detective in 1987.
His illustrious theatre career also included appearances in Alan Ayckbourn’s The Norman Conquests, The Life Of Galileo and Nicholas Hytner’s National Theatre production of Henry IV, Parts 1 and 2.
Harry Potter creator JK Rowling also paid tribute, saying she first saw him perform in King Lear in 1982 and if someone had told her he “would appear in anything I’d written, I’d have thought you were insane”.
Dame Helen Mirren recalled working alongside him in 1982’s Antony And Cleopatra, and said he made an “extraordinary contribution to the British landscape of theatre”.
Sir Michael was also known for playing French detective Jules Maigret in ITV series Maigret, and for his role as Philip Marlow in Dennis Potter’s The Singing Detective. He made his first appearance on stage in a production of Othello in Dublin in 1962 when he returned to Ireland following his move to the UK.
His later film roles also included period dramas such as 2010’s The King’s Speech, 2001’s Gosford Park and 2017’s Victoria & Abdul.
He was recognised with Emmy nominations, including for Mr Woodhouse in a 2010 adaptation of Jane Austen’s Emma and as former US president Lyndon B Johnson in Path To War in 2002.
In 1990 he won an Olivier Award for comedy performance of the year in Man Of The Moment at the Globe. He was knighted in 1998 for his contribution to entertainment.