He made his first-class debut for Oxford University about halfway through the 1952 university cricket season and hit 53 in his first match, against Sussex in The Parks.[8] In the return match at Worthing, he made 74, but he did not retain his place and he was not selected for the University Match against Cambridge.[9] When the university cricket season was over, Williams played for Oxfordshire in the Minor Counties.
In 1953, Williams played regularly for the university side and in the match against Free Foresters, an itinerant amateur side of varying quality whose matches against the universities were considered first-class at this time, he made his first century, scoring 115 in a match ruined by rain.[10] In the University Match, he made 40 and 5 as Oxford lost by two wickets in a close finish.[11]
The 1954 season saw Williams achieve 1,000 runs in the season for the first time: he finished with 1128 at an average of 30.48 runs per innings.[7] He was particularly successful for Oxford University, batting generally at No 3 and scoring 115 against Lancashire and then an unbeaten 139 followed by 89 in the second innings in the match against Hampshire.[12][13] He was not successful in the University Match, batting just once and scoring 14.[14] Later in the summer, he played in 11 matches for Essex, but his highest score for the county was only 54.
Williams was captain of the Oxford University cricket team in his final year at the university, 1955. The team was not successful, failing to win any of its first-class matches, and Williams' captaincy attracted some criticism in Wisden Cricketers' Almanack.[15] "The weather was certainly against them, and in all their ten home games none was played through without some interference from rain and, altogether, nine and a half days of playing time were lost," Wisden wrote. "That in itself may have undermined the determination of the side, though a more likely handicap to the individual players was the length of time C. C. P. Williams took to decide who would be in the XI to meet Cambridge. The freshmen were particularly affected and when the weeks passed and they were still playing for their places none of them was able to relax and play a natural game."[15]
Williams started the season well with 120 in the first match, against Gloucestershire.[16] But his form declined and Oxford had the worse of a drawn University Match, though Williams' own second innings 47 not out helped save the game for his side.[17] After the university season was over, he again played for Essex, and scored his first century in County Championship cricket, making 119 and sharing a fourth-wicket partnership of 200 with Doug Insole in the match against Leicestershire at Leicester.[18] The 1955 season was, in all, Williams' most successful: he made 1219 runs at an average of 31.25, both his highest seasonal aggregate and average.[7]
In 1956 and 1957, Williams was on National Service. In the 1956 season, he played a couple of matches for the Combined Services cricket team, making an unbeaten 125 in the match against Warwickshire.[19] There were also a few matches in this season for Essex and one for Marylebone Cricket Club (MCC) at Lord's; at the end of the season, he played in two matches at the Scarborough Festival, one for MCC against Yorkshire in which he was used unsuccessfully as an opening batsman, and the second the Gentlemen v Players match in which he made 0 and 1.[20][21] These were his only games of representative cricket. In 1957, he played no first-class cricket at all.
Williams returned to first-class cricket in the second half of the 1958 season, playing 10 matches for Essex and adding what Wisden called "extra stability" to the county's batting.[22] In 1959, he reappeared for four matches, but with no success, and these were his final first-class matches.
Williams had been an amateur cricketer and played for the Gentlemen against the Players. Social change after the Second World War led to a reaction against the cricketing concept of amateurism, often disparaged as "shamateurism", and in 1963 all first-class cricketers became nominally professional as, in effect, "Players". The last edition of the annual Gentlemen v Players fixture was at Scarborough in September 1962. The events leading to the abolition of amateurism are described by Williams in his 2012 book, Gentlemen & Players, appropriately subtitled The Death of Amateurism in Cricket.
In the 1964 General Election, Williams stood unsuccessfully for Parliament as the Labour Party candidate for Colchester. In 1976 he unsuccessfully attempted to become the Labour candidate for the Vauxhall constituency.[23]