Born in London, the former Northampton Town trainee moved to the United States on a football scholarship after giving up on football in England. Blackwood started his scholarship at the University of Tampa. Blackwood played two seasons at the university, making 33 appearances for the Spartans scoring 24 goals and racking up 8 assists. Blackwood also received both the player of the year, and offensive player of the year award two years running, breaking several records at the university. Whilst at the University Of Tampa Blackwood also took part in the summerPDL league for Orlando City U-23. He went on to score 15 goals in 14 games for the Lions, finishing #1 in the nation in goals. For his final year of collegiate eligibility Blackwood transferred to nearby NCAA Division 1 school University of South Florida. Blackwood played 18 games for the Bulls, scoring 4 goals and making 3 assists. Blackwood was overlooked for the 2015 MLS draft, and returned to England and earned a trial at Queens Park Rangers. He successfully impressed during his trial, and signed his first professional deal with QPR.
After impressing during a trial, on 10 July 2015 Blackwood signed a one-year deal starting from 1 August 2015 with Queens Park Rangers. Blackwood scored six goals in total during his first spell with Rangers at the tail end of the previous 2014–15 season, before signing for the club, including a match-winning brace for the Under-21s at Crewe Alexandra and another double in a first team friendly with Norwich City. On 12 August 2015 Blackwood made his professional debut in Queens Park Rangers 0–3 win over Yeovil Town in the first round of the 2015–16 Football League Cup as a substitute replacing Matt Phillips in the 70th minute at Huish Park.
On 24 September 2015 Blackwood joined League Two club Newport County on a one-month loan. He made his debut for Newport on 26 September as a 60th-minute substitute in a match against Carlisle United. In the 68th minute Blackwood scored a headed goal and Newport went on to win the match 1–0.