The four British art critics mentioned in the crossword solutions are TATE, ELIE, CLIVE, and RUSKIN. John Ruskin (1819-1900) was an influential art critic, social thinker, and philanthropist who wrote extensively on the importance of art and its role in society. CLIVE Bell (1881-1964) was a British art critic and member of the Bloomsbury Group, a circle of writers, intellectuals, and artists. Elie Faure (1873-1937) was a French art critic and historian who wrote extensively about modern art. Lastly, Sir John Rothenstein (1892-1992) was an English art historian, director of the Tate Gallery, and author of several books on British art.