Wilson was a champion junior player, winning the 1951 British Junior Championship at age 15. He was runner-up the following two years as well as doubles champion partnering Billy Knight. Whilst still a junior Wilson won senior level singles matches at Wimbledon - in 1952 he lost to eventual runner-up Jaroslav Drobný in the second round whilst the following year he reached the third round, where he went out to eventual quarter-finalist Sven Davidson in five sets.
Wilson first reached a major quarter-final in 1958, at Wimbledon. Unseeded, he reached the round without dropping a set, setting up a meeting against No. 1 seed Ashley Cooper. The champion Australian took the first two sets handily before Wilson stormed back to level matters at 2 sets apiece. The deciding set was closely contested with eventual champion Cooper prevailing 7-5. Wilson, seeded No. 4, reached the same stage the following summer but went out without much of a stir to Roy Emerson in straight sets.
1960 saw Wilson, the No. 8 seed, reach the quarter-finals at the U.S. Nationals in his fourth appearance at Forest Hills. He breezed to the final 8 without dropping a set, after defeating Allen Fox in the round of 16. He next met No. 2 seed Rod Laver. Despite hanging close in the opening set, Wilson went down easily to the future tennis legend in three straight sets. Wilson reached the quarters yet again at Wimbledon the following summer, but not without some drama. He barely survived his first round match versus Argentine Eduardo Soriano, coming back from 2 sets to 1 down to prevail, 6-2, 4-6, 5-7, 16-14, 6-3. Two rounds later, Wilson scored perhaps the biggest match victory of his career, dispatching No. 1 seed Neale Fraser 1-6, 6-0, 13-11, 9-7. The following round, however, proved once again to be a roadblock for Wilson as he went out to No. 8 seed Chuck McKinley in four sets.
1963 proved to be Wilson's best year as he reached the quarter-finals at Roland Garros, Wimbledon, and Forest Hills. In Paris, Wilson, as he often did when he went far into tournaments, breezed through the first four rounds, including a round of 16 win over No. 6 seed Bob Hewitt. As was his wont too, however, he went out rather easily in the next round, this time to French champion and No. 3 seed Pierre Darmon. A month later, again unseeded, Wilson once more made it to the quarter-finals, but was easily beaten by the No. 4 seed Chuck McKinley. His success for the year saw him seeded No. 6 at Forest Hills and he succeeded in justifying this seeding, as he, once again, raced into the quarter-finals. His opponent this time, however, was not a big name, unseeded Frank Froehling. Taking the first two sets, Wilson looked primed to reach his first major semi-final, but he lost the next two sets. Froehling took the deciding set too, however, by a score of 9 games to 7, saving a match point to do so.
Even when past his prime, Wilson continued to compete at Wimbledon, if only in doubles. He took eventual finalist Wilhelm Bungert to 7-9 in the fifth set of their fourth round encounter in 1967 and in 1969 reached the fourth round, for the last time, in both singles and doubles. His final Wimbledon was in 1977, where at age of 41 he played in the mixed doubles and lost in the first round - he played just in the doubles draw from 1971 onwards. Overall he played in 124 matches at Wimbledon winning 77 and losing 47.
Between 1955 and 1968 Wilson participated in 34 ties for the British Davis Cup team. He compiled a record of 40 wins versus 20 losses and had a better record in doubles (25–8) than singles (16–12). The most successful year was 1963 when the British team won the Europe Zone, defeating Sweden in the final, to reach the Inter-Zonal semifinal against the United States.
Wilson coached locally in his post-tour days.
In 1964 Wilson published a book titled My Side of the Net. As of 1981, Wilson was a resident of Finchley, Greater London, where he also lived as a boy.