Jenkinson was a right-handed batsman played primarily as a wicketkeeper. Jenkinson made his first-class debut for Essex in the 1922 County Championship against Hampshire at the United Services Recreation Ground, Portsmouth. From 1922 to 1923, he represented the county in 5 first-class matches, the last of which came against Middlesex.
In his 5 first-class matches, he scored 9 runs at a batting average of 2.25, with a high score of 8.
Behind the stumps he took 4 catches and made 4 stumpings. He died at Pembury, Kent on 6 November 1980.