In the Southern Hemisphere winter in 1959, Simpson played a season in the Lancashire League in England as Accrington's professional player, receiving a 950-pound contract. He scored 1,444 runs at 103.14, returning a better statistical analysis than Gary Sobers, and took 47 wickets at 20.82. Simpson's top-score of 122 not out came against Ramsbottom and added another triple-figure score against Bacup, and his season included 11 consecutive fifties including a century, seven of which were unbeaten. In all, he scored two centuries and 14 fifties in 26 innings. He took five-wicket hauls three times with a best of 6/40 against Nelson.