In 1876 the 'Brighton School of Art' moved to a new, yellow-brick, Italianate building in Grand Parade, seen just to the right of the trees, and became the 'School of Art & Science'. Since then it has had many names but College of Art seem a good approximation. It was enlarged in 1910 & 1914 and demolished in 1965 along with neighbouring properties.
The replacement building to a design by the Borough Architect, Percy Billington, opened in 1967. It has a gently-curved frontage which follows the line of the road and the design is generally admired. It now comprises one of the campuses of the Faculty of Arts of the University of Brighton.
(It looks like the same tree in both photos but I don't see how it can be. In the 100 or so years that have elapsed it would surely now be of much larger girth.)