Cegielski started his career at Tottenham Hotspur in May 1973, and was a member of the FA Youth Cup winning side of 1974. However he didn't play a First Division game for Terry Neill's side, and was instead loaned out to Fourth Division side Northampton Town. He played eleven league games for Bill Dodgin's "Cobblers". He left White Hart Lane in 1975, and linked up with German side VfB Stuttgart. He played five games in 2. Bundesliga for István Sztáni's "Reds" in 1975–76, before he departed for the United States to play for Tacoma Tides in the ASL. He returned to the UKin September 1976, and signed with Third Division Wrexham, then managed by John Neal. The "Red Dragons" finished fifth in 1976–77, one point behind promoted Crystal Palace. Arfon Griffiths took the reins for the 1977–78 campaign, and Wrexham topped the division with 61 points. Wrexham retained their Second Division status in 1978–79, and qualified for the European Cup Winners' Cup after reaching the final of the Welsh Cup, where they lost out to Shrewsbury Town. A mid-table finish followed in 1979–80, before they avoided relegation in 1980–81 by just two points. Mel Sutton took charge for the 1981–82 campaign, however this time the club finished two points away from safety, and were relegated back into the third tier. Cegielski left Wrexham with 123 league appearances to his name, and joined John McGrath's Fourth Division Port Vale in July 1982. He quickly slotted into the squad and was a regular in the 1982–83 promotion winning season, picking up the Player of the Year award at the end of the campaign. During the season he hit five goals in 48 games, striking in wins against Hereford United, Halifax Town, Crewe Alexandra, Aldershot, and Peterborough United. He then played 43 games in 1983–84, as the club suffered relegation. He fell out of favour under John Rudge in 1984–85, as Phil Sproson and Alan Webb built up a partnership. Cegielski was allowed to move to Blackpool on a free transfer in March 1985. In six games for Sam Ellis' club, he scored one goal – Blackpool's first in a 6–1 victory over Crewe Alexandra at Bloomfield Road on 9 April 1985. The "Tangerines" won promotion out of the Fourth Division as runners-up, but he was not retained beyond the end of the season. He then linked up with manager Johnny Newman at Hereford United, and made a total of 66 appearances for the club in league and cup. The "Bulls" finished in mid-table in the fourth tier in 1985–86 and 1986–87, after which Cegielski left the Football League for non-league Worcester City. He later turned out for Northwich Victoria.
