Laurence Olivier's peerage was announced in the 1970 Birthday Honours, and Andrew Lloyd Webber's in the 1997 New Year Honours. There have been no peerages in honours lists since the 2000 New Year Honours. In 2001 the nomination of Crossbench peers was passed to the House of Lords Appointments Commission (HOLAC), and although the restriction on the Prime Minister's nomination of non-party peerages has been progressively watered down since then (and HOLAC has in recent times been limited to an average of two nominations a year) it seems unlikely that a "celebrity" would be nominated except (1) as a political nomination, as with Ian Botham (Lord Botham 2020), or (2) through HOLAC, which would require a commitment to play an active part in the House of Lords.
Past HOLAC nominations of people from "the arts" include Michael Berkeley (Lord Berkeley of Knighton, 2013) and Deborah Bull (Baroness Bull, 2018).
Other pre-2001 creations of life peers from the arts include Benjamin Britten (Lord Britten, 1976), Bernard Miles (Lord Miles, 1979) and Yehudi Menuhin (Lord Menuhin, 1993).