Between 1895 and 1901, Atkins played in seven minor tournaments, winning four and finishing second or equal second in the others, and losing just 3 out of 70 games. These included the minor tournament at the great Hastings 1895 tournament, where he finished equal second, behind Géza Maróczy, and was awarded the Newnes Cup for the best result by a British amateur. At Bristol 1896, he yielded just one draw in nine games. At Southampton 1897, the Eighth British Amateur Championship, he scored an undefeated 8.5 points out of 10 possible, retaining his British amateur title. At Craigside 1899, he scored 7.5/10, behind Amos Burn (9/10). At Amsterdam 1899, an amateur tournament that was Atkins' first international appearance, he achieved a rare perfect score, winning all 15 games and finishing 4 points ahead of the second-place finisher. He scored 4/6, again finishing behind Burn (5/6), at Birmingham 1899. At Bath 1900, he scored 12.5/14, yielding just 3 draws in 14 games. At Llandudno 1901, a four-man double-round robin, Atkins was again bested by Burn, who scored 4.5/6 to Atkins' 3.5 points. Between 1896 and 1911, Atkins participated in the annual 10-board cable match between Britain and the United States every year except 1909.