Cook was born in Wath upon Dearne, a mining and market town in the Dearne Valley near Rotherham in South Yorkshire. He came from a motorsport-interested family: his sister Paula was racing in British Formula 3 at the same time he was competing in Formula Renault and later Formula 3000 in the mid-1990s. The coincidence of a brother and sister ascending the British junior single-seater ladder simultaneously attracted press attention at the time, particularly when Cook entered the series directly below Formula One while Paula was still active in the tier below. The combination of two Cook siblings in open-wheel racing at once was unusual and made the family notable in the small world of British junior motorsport.
Cook made his car-racing debut in British Formula Vauxhall Junior in 1994, gaining his first experience of single-seater competition. He moved to British Formula Renault in 1995 and finished sixth in the championship in his first full season at that level. Returning to Formula Renault in 1996, he improved substantially across the year and won the championship outright. The title was the most competitive rung of the domestic single-seater ladder below Formula Three and identified Cook as one of the leading young British open-wheel talents of the 1996 season.
In 1997 Cook entered the FIA Formula 3000 International Championship — the single series operating directly below Formula One in the FIA's global ladder at that time — and did so not as a driver in an established team but as the operator of his own: DC Cook Motorsport. Running a Lola T96/50 chassis with a Zytek engine, he contested six of the ten championship rounds. Setting up and funding a team whilst simultaneously racing in it at the Formula 3000 level was an unusual and demanding undertaking for a driver still in his early twenties, requiring parallel management of competitive, mechanical, and financial responsibilities.
For 1998 Cook stepped back from the team-owner role and joined Redman Bright as a driver, making one start from the twelve-round calendar, again in a Lola T96/50-Zytek. He made eight Formula 3000 starts in total across his two seasons in the series and did not return to the championship for 1999, effectively ending his competitive career as a racing driver at that point.
Cook competed during a period when the British Formula Renault championship was a well-regarded springboard toward Formula 3000 and Formula Three. Several alumni of that era's Formula Renault title — in seasons either side of 1996 — went on to careers in Formula One, so Cook's championship, while not leading to a Formula One career, placed him in a competitive cohort. The FIA Formula 3000 series of 1997–1998 included drivers who reached Formula One, and Cook competed against that field across his eight starts.
Following his retirement from competitive driving Cook returned to Rotherham and developed business interests that retained a partial connection to motorsport. He operated a motorsport parts business and a leasing company. In the early 2010s he channelled his attention toward supporting his nephew Jake in Formula Renault at the junior level, continuing the family's multi-generational involvement in British single-seater competition.
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