In the doubles, he partnered with Major Ritchie and, after a bye in the quarter-finals, reached the semifinal in which they were defeated by compatriots Arthur Gore and Herbert Roper Barrett.

They subsequently lost the match for third place and the bronze medal against Wollmar Boström and Gunnar Setterwall.

[2] Escombe's best performance at a Grand Slam tournament was reaching the quarter final in the men's singles event at the 1907 Wimbledon Championships, which he lost in five sets to Wilberforce Eaves.

He equaled this performance at the 1907 Wimbledon Championships, this time losing to Herbert Roper-Barrett in straight sets.

[3] In 1909, he was runner-up in the men's singles event at the South African Championships, losing in the final to compatriot and multiple Wimbledon champion Reginald Doherty in straight sets.