Legend has it that the name itself originated from a chance remark by the actress Alice Delysia, who overheard Giandolini apologise to a customer for the inconvenience caused by building works.

In part due to its proximity to the West End theatres, exclusivity and late closing time, the restaurant quickly became a theatrical institution, with Laurence Olivier and Vivien Leigh, Marlene Dietrich, John Gielgud, Lilian Braithwaite, Terence Rattigan, Binkie Beaumont and Noël Coward being habitués, having their regular two-seater tables along the walls.

According to the actor Donald Sinden in his Sky Arts television documentary series Great West End Theatres, The Ivy became so famous as a theatrical-celebrities haunt that in the 1943 revue Sweet and Low which ran for almost six years at the neighbouring Ambassadors Theatre, there was a satirical sketch included, updated regularly, entitled Poison Ivy, where the show's star Hermione Gingold "would exchange wicked and salacious celebrity gossip".

Mobile phones and cameras are forbidden throughout the restaurant and adjoining club and there is a dress code requiring smart casual attire.

[11][12] It has a Piano Lounge; a dining room ("The Drawing Room"), open for breakfast, lunch and supper; a wood-panelled library "of books that reflect many of our members' interests in art, literature, film, theatre, architecture and design"; a film screening-room and entertainment space known as the Loft; a further private dining-room seating up to 14 people and a cigar-terrace.

[13] Its former director was Fernando Peire who left in June 2021, the former senior maître d' (star of the Channel 5 TV series The Restaurant Inspector).

[16] Multiple branches have opened across the UK since, including Cardiff, Brighton, London (Chelsea, Mayfair and St Paul's) and Leeds.