Arkinstall had a lengthy amateur tennis player, and traveled the world. He won numerous matches and international tennis tournaments, however never reached the top of his country. At Wimbledon, he reached the fourth round in 1953 when he was in the fifth set against in his compatriot Ken Rosewall, whom he had lost against previously. At Wimbledon in 1954 Arkinstall lost in the first round against the eventual champion, Yugoslav Jaroslav Drobny. He competed again in 1955 at Wimbledon, this time reaching the third round to fall against Drobny. At Wimbledon in 1956, Arkinstall lost to the eventual semifinalist, American Ham Richardson. In his last appearance at Wimbledon 1957, he lost in the first round in a large defeat against the Brit Mike Davies. He never won the Australian Open Championships or any other Grand Slam tournament. Once he played against Rosewall in his professional career and lost narrowly in the final, fifth set. Arkinstall broke through late into international tennis. In 1950, when he was thirty years old, he played his first internationaltennis tournament. In 1954 Arkinstall won in the final against the number one player from India Ramanathan Krishnan. He won the Yugoslavian Championships that year against the number one Yugoslav Jaroslav Drobny. In an indoor tournament India Krishnan revenged himself by winning the final against Arkinstall. In 1956 Arkinstall played the Nation Cup for his country - he lost the men's doubles match with Lew Hoad against his Italian opponents Guiseppo Merlo and Orlando Sirola.
Professional career
In 1958 he played as a professional in his debut at the Wembley Championships in London when he lost the first round of his compatriot Frank Sedgman. The year after Arkinstall played back on Wembley Championships and he again lost against compatriot Ashley Cooper. At the French Pro Championship in 1959 Arkinstall was defeated in the fourth round and repeated that at the tournament in 1960. In 1960 Arkinstall played at the Wembley Pro and again lost in the first round, this time against the Spaniard Andrés Gimeno, the Spanish number one. In 1962, he competed as a pro in the US Pro Championships reaching the quarterfinal against Earl Buchholz. That was his last year in professional tennis.
In memory of the Arkinstall family, a sports centre, Arkinstall Park, exists at Tweed Heads, Australia. Upgrades to the park's existing facilities were announced in 2013. The park includes netball courts and clubhouse, tennis courts and clubhouse, BBQ area and playground. Note: Arkinstall park in Hefron St South Tweed Heads was actually named after Jack's younger brother Neville who was a talented sprotsman in his own right being accomplished as a Hockey and cricket player as well as tennis.
