Matters changed for Barber in the 1932 season, when Yorkshire's regular, long serving opening batsman Percy Holmes began to suffer with illness. This left a batting place empty and enabled Barber to play more regularly. "Wisden Cricketer's Almanack" believed that he thoroughly deserved his place in the team as he scored exactly 1,000 runs at an average of 25.64, the first time he reached four figures in a season. He finished fifth in the Yorkshire batting averages, the first time he had been placed so high. His runs also played a part in Yorkshire winning the County Championship in his first full season. After this breakthrough, Barber steadily improved his total of runs and batting average, helping Yorkshire to win the County Championship twice in 1933 and 1935. In 1933, he scored 1,595 runs at an average of 33.93, and in 1934 he scored 1,927 runs at an average of 40.14. In both seasons he finished fourth in the Yorkshire averages. However, Barber's best season statistically was the following season, 1935, when he achieved his best aggregate of runs and highest average in an English season, passing 2,000 runs in a season for the only time in his career. He scored 2,147 runs at an average of 42.09 and finished third in the Yorkshire averages. These performances earned him selection for the Players against the Gentlemen at Lord's Cricket Ground for the only time in his career, where he scored 61 and 18 not out.