 Grove became an experienced alpinist in the late 1850s and joined the Alpine Club of London soon after it was formed in 1857, later serving as its President from 1884 to 1886.He was one of the best British climbers of his day and is remembered for opposing guideless climbing during the 1870s.An article on the founders of the Alpine Club in the Oxford Dictionary of National Biography calls him a "gentleman traveller of independent means".